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:

Solve using the quadratic formula.\newline4w2+4w+1=04w^2 + 4w + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinew=w = _____ or w=w = _____

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Solve a quadratic equation using the quadratic formularight chevron icon

Full solution

Q. Solve using the quadratic formula.\newline4w2+4w+1=04w^2 + 4w + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinew=w = _____ or w=w = _____
  1. Identify coefficients: Identify the coefficients of the quadratic equation.\newlineThe quadratic equation is in the form aw2+bw+c=0aw^2 + bw + c = 0. For the given equation, 4w2+4w+1=04w^2 + 4w + 1 = 0, the coefficients are:\newlinea = 44, b = 44, and c = 11.
  2. Write formula: Write down the quadratic formula.\newlineThe quadratic formula is w=−b±b2−4ac2aw = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Substitute coefficients: Substitute the coefficients into the quadratic formula.\newlineUsing the values of aa, bb, and cc from Step 11, we get:\newlinew=(−(4)±(4)2−4(4)(1))/(2(4))w = (-(4) \pm \sqrt{(4)^2 - 4(4)(1)}) / (2(4)).
  4. Simplify discriminant: Simplify the expression under the square root (the discriminant).\newlineCalculate the discriminant: (4)2−4(4)(1)=16−16=0(4)^2 - 4(4)(1) = 16 - 16 = 0.
  5. Simplify formula: Simplify the quadratic formula with the discriminant.\newlineSince the discriminant is 00, the square root of 00 is 00, so the formula simplifies to:\newlinew=−4±08w = \frac{-4 \pm 0}{8}.
  6. Solve for w: Solve for w.\newlineSince the ±\pm term is 00, we only have one solution:\newlinew=(−4)/8w = (-4) / 8.\newlineSimplify the fraction:\newlinew=−12w = -\frac{1}{2}.

More problems from Solve a quadratic equation using the quadratic formula

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 (78)

Related topics

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