Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find one value of x that is a solution to the equation: {:[(7x+2)^(2)+6(7x+2)=27],[x=◻]:}

Find one value of x x that is a solution to the equation:\newline(7x+2)2+6(7x+2)=27x=□ \begin{array}{l} (7 x+2)^{2}+6(7 x+2)=27 \\ x=\square \end{array}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Solve a quadratic equation by factoringright chevron icon

Full solution

Q. Find one value of x x that is a solution to the equation:\newline(7x+2)2+6(7x+2)=27x=□ \begin{array}{l} (7 x+2)^{2}+6(7 x+2)=27 \\ x=\square \end{array}
  1. Expand and distribute: Let's first expand the squared term and distribute the 66 in the equation (7x+2)2+6(7x+2)=27(7x+2)^2 + 6(7x+2) = 27.(7x+2)2(7x+2)^2 becomes (7x+2)(7x+2)(7x+2)(7x+2) which is 49x2+14x+14x+449x^2 + 14x + 14x + 4.6(7x+2)6(7x+2) becomes 42x+1242x + 12. So the equation now is 49x2+14x+14x+4+42x+12=2749x^2 + 14x + 14x + 4 + 42x + 12 = 27.
  2. Combine like terms: Combine like terms in the equation. \newline49x2+14x+14x+42x+4+12=27.49x^2 + 14x + 14x + 42x + 4 + 12 = 27.\newlineThis simplifies to 49x2+70x+16=27.49x^2 + 70x + 16 = 27.
  3. Set equation to zero: Subtract 2727 from both sides to set the equation to zero.\newline49x2+70x+16−27=0.49x^2 + 70x + 16 - 27 = 0.\newlineThis simplifies to 49x2+70x−11=0.49x^2 + 70x - 11 = 0.
  4. Use quadratic formula: Now we need to solve the quadratic equation 49x2+70x−11=049x^2 + 70x - 11 = 0. This does not factor easily, so we will use the quadratic formula, x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2-4ac}}{2a}, where a=49a = 49, b=70b = 70, and c=−11c = -11.
  5. Calculate discriminant: First, calculate the discriminant, which is b2−4acb^2 - 4ac.\newlineThe discriminant is 702−4(49)(−11)70^2 - 4(49)(-11).\newlineThis is 4900+21564900 + 2156.\newlineThe discriminant is 70567056.
  6. Solve for x: Since the discriminant is positive, we have two real solutions. Now we calculate the solutions using the quadratic formula.\newlinex=−70±70562⋅49x = \frac{{-70 \pm \sqrt{7056}}}{{2 \cdot 49}}.
  7. Calculate square root: Calculate the square root of the discriminant. 7056=84\sqrt{7056} = 84.
  8. Plug square root into formula: Now plug the square root back into the quadratic formula. x=−70±8498x = \frac{{-70 \pm 84}}{{98}}.
  9. Simplify solutions: We have two potential solutions for x: x=−70+8498x = \frac{-70 + 84}{98} and x=−70−8498x = \frac{-70 - 84}{98}. The first solution simplifies to x=1498x = \frac{14}{98}, which reduces to x=17x = \frac{1}{7}. The second solution simplifies to x=−15498x = \frac{-154}{98}, which reduces to x=−7749x = -\frac{77}{49}.
  10. Choose a solution: We have found two values of xx that satisfy the equation. We can choose either one as the answer to the question prompt. Let's choose the simpler one, x=17x = \frac{1}{7}.

More problems from Solve a quadratic equation by factoring

Question
Solve for v v .\newlinev2+8v+12=0 v^2+8v+12=0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinev= v=_____
Get tutor helpright-arrow

Posted 3 months ago

Question
Solve for u u .\newlineu2=9 u^2 = 9 \newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlineu= u = _____ or u= u = _____
Get tutor helpright-arrow

Posted 8 months ago

Question
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinek2−20k+_____k^2 - 20k + \_\_\_\_\_
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve by completing the square.\newlineu2−24u−23=0u^2 - 24u - 23 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`u` = ________ or `u` =______
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the discriminant. \newline2q2−9q+8=02q^2 - 9q + 8 = 0\newline______
Get tutor helpright-arrow

Posted 4 months ago

Question
Solve the system of equations.\newliney=22x−38 y = 22x - 38 \newliney=x2+11x−14 y = x^2 + 11x - 14 \newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(_,_) (\_,\_) \newline(_,_) (\_,\_)
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve for aa.\newline(a+5)(a+1)=0(a + 5)(a + 1) = 0\newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlinea=a = _____ or a=a = _____
Get tutor helpright-arrow

Posted 8 months ago

Question
Let p=x2−7 p=x^{2}-7 . Which equation is equivalent to (x2−7)2−4x2+28=5 (x^{2}-7)^{2}-4x^{2}+28=5 in terms of p p ? Choose 11 answer: \newline(A) p2−4p+23=0 p^{2}-4p+23=0 \newline(B) p2+4p−5=0 p^{2}+4p-5=0 \newline(C) p2−4p−5=0 p^{2}-4p-5=0 \newline(D) p2+4p+23=0 p^{2}+4p+23=0
Get tutor helpright-arrow

Posted 8 months ago

Question
Let m=2x+3m=2x+3. Which equation is equivalent to (2x+3)2−14x−21=−6(2x+3)^{2}-14x-21=-6 in terms of mm? Choose 11 answer: \newline(A) m2+7m+6=0m^{2}+7m+6=0 \newline(B) m2−7m−15=0m^{2}-7m-15=0 \newline(C) m2−7m+6=0m^{2}-7m+6=0 \newline(D) m2+7m−15=0m^{2}+7m-15=0
Get tutor helpright-arrow

Posted 8 months ago

Question
Let m=x2+3m=x^{2}+3. Which equation is equivalent to (x2+3)2+7x2+21=−10(x^{2}+3)^{2}+7x^{2}+21=-10 in terms of mm? Choose 11 answer:\newline(A) m2−7m+31=0m^{2}-7m+31=0\newline(B) m2+7m+31=0m^{2}+7m+31=0\newline(C) m2−7m+10=0m^{2}-7m+10=0\newline(D) m2+7m+10=0m^{2}+7m+10=0
Get tutor helpright-arrow

Posted 9 months ago

View all (122)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant