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: {:[(x^(2)+3)^(2)+21=10x^(2)+30],[x=◻]:}

Find one value of x x that is a solution to the equation:\newline(x2+3)2+21=10x2+30x=□ \begin{array}{l} \left(x^{2}+3\right)^{2}+21=10 x^{2}+30 \\ 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(x2+3)2+21=10x2+30x=□ \begin{array}{l} \left(x^{2}+3\right)^{2}+21=10 x^{2}+30 \\ x=\square \end{array}
  1. Expand left side of equation: We are given the equation (x2+3)2+21=10x2+30(x^2 + 3)^2 + 21 = 10x^2 + 30. Let's start by expanding the left side of the equation.\newline(x2+3)2=x4+6x2+9(x^2 + 3)^2 = x^4 + 6x^2 + 9\newlineNow, we rewrite the equation with the expanded form:\newlinex4+6x2+9+21=10x2+30x^4 + 6x^2 + 9 + 21 = 10x^2 + 30
  2. Rewrite equation with expanded form: Next, we simplify the equation by combining like terms on the left side: x4+6x2+30=10x2+30x^4 + 6x^2 + 30 = 10x^2 + 30
  3. Combine like terms on left side: Now, we subtract 10x210x^2 and 3030 from both sides to move all terms to one side and set the equation to zero:\newlinex4+6x2+30−10x2−30=0x^4 + 6x^2 + 30 - 10x^2 - 30 = 0
  4. Move terms to one side and set equation to zero: Simplify the equation by combining like terms: x4−4x2=0x^4 - 4x^2 = 0
  5. Factor out x2x^2 from equation: We can factor out an x2x^2 from the equation:\newlinex2(x2−4)=0x^2(x^2 - 4) = 0
  6. Apply zero-product property: Now we have a product of two factors equal to zero. We can use the zero-product property to set each factor equal to zero:\newlinex2=0x^2 = 0 or x2−4=0x^2 - 4 = 0
  7. Solve first equation for x: Solving the first equation for x gives us:\newlinex=0x = 0
  8. Solve second equation for x: Solving the second equation for x gives us two solutions because it is a difference of squares:\newlinex2−4=(x+2)(x−2)=0x^2 - 4 = (x + 2)(x - 2) = 0\newlineSo, x=−2x = -2 or x=2x = 2

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