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 by completing the square.\newlinew2+2w=3w^2 + 2w = 3\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
Algebra 2right chevron icon
Solve a quadratic equation by completing the squareright chevron icon

Full solution

Q. Solve by completing the square.\newlinew2+2w=3w^2 + 2w = 3\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. Rewrite Equation: Rewrite the equation in the form of w2+bw=cw^2 + bw = c. We have the equation w2+2w=3w^2 + 2w = 3. To complete the square, we need to have a constant term on the left side that makes it a perfect square trinomial.
  2. Find Constant Term: Find the number to add to both sides to complete the square.\newlineWe take half of the coefficient of ww, which is 22, divide it by 22 to get 11, and then square it to get 12=11^2 = 1.\newlineAdd 11 to both sides of the equation to complete the square.\newlinew2+2w+1=3+1w^2 + 2w + 1 = 3 + 1\newlinew2+2w+1=4w^2 + 2w + 1 = 4
  3. Factor Perfect Square Trinomial: Factor the left side as a square of a binomial.\newlineThe left side is now a perfect square trinomial, which factors into (w+1)2(w + 1)^2.\newline(w+1)2=4(w + 1)^2 = 4
  4. Take Square Root: Take the square root of both sides.\newlineTo solve for ww, we take the square root of both sides of the equation.\newline(w+1)2=±4\sqrt{(w + 1)^2} = \pm\sqrt{4}\newlinew+1=±2w + 1 = \pm2
  5. Solve for w: Solve for w.\newlineWe now have two equations to solve for w:\newlinew+1=2w + 1 = 2 and w+1=−2w + 1 = -2.\newlineFor the first equation:\newlinew+1=2w + 1 = 2\newlinew=2−1w = 2 - 1\newlinew=1w = 1\newlineFor the second equation:\newlinew+1=−2w + 1 = -2\newlinew=−2−1w = -2 - 1\newlinew=−3w = -3

More problems from Solve a quadratic equation by completing the square

Question
Solve by completing the square.\newlinem2−10m−29=0m^2 - 10m - 29 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`m` = ____ or `m` = _____
Get tutor helpright-arrow

Posted 8 months ago

Question
Find g(x) g(x) , where g(x) g(x) is the translation 5 5 units up of f(x)=x2 f(x)=x^2 .\newlineWrite your answer in the form a(x–h)2+k a(x–h)^2+k , where a a , h h , and k k are integers.\newlineg(x)= g(x)= ____
Get tutor helpright-arrow

Posted 7 months ago

Question
What is the range of this quadratic function?\newliney=x2−4x+4y = x^2 - 4x + 4\newlineChoices:\newline{y∣y≥2}\left\{y \mid y \geq 2\right\}\newline{y∣y≤0}\left\{y \mid y \leq 0\right\}\newline{y∣y≥0}\left\{y \mid y \geq 0\right\}\newlineall real numbers\text{all real numbers}
Get tutor helpright-arrow

Posted 5 months ago

Question
Write the equation of the parabola that passes through the points (1,0)(1,0), (2,0)(2,0), and (3,–16)(3,\text{–}16). Write your answer in the form y=a(x–p)(x–q)y = a(x – p)(x – q), where aa, pp, and qq are integers, decimals, or simplified fractions.\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinef2+8f+_____f^2 + 8f + \_\_\_\_\_
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve for h h .\newlineh2+39h=0 h^2 + 39h = 0 \newline\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlineh= h = ____\newline
Get tutor helpright-arrow

Posted 5 months ago

Question
Write a quadratic function with zeros −9-9 and −7-7.\newlineWrite your answer using the variable xx and in standard form with a leading coefficient of 11.\newlinef(x)=_____f(x) = \_\_\_\_\_
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the equation of the axis of symmetry for the parabola y=x2y = x^2. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline‾\underline{\hspace{3cm}}
Get tutor helpright-arrow

Posted 4 months ago

Question
Find g(x)g(x), where g(x)g(x) is the translation 88 units up of f(x)=x2f(x) = x^2.\newlineWrite your answer in the form a(x–h)2+ka(x – h)^2 + k, where aa, hh, and kk are integers.\newlineg(x)=g(x) = ______\newline
Get tutor helpright-arrow

Posted 4 months ago

Question
Solve for xx.\newlinex2=1x^2 = 1\newline\newlineWrite your answer in simplified, rationalized form.\newlinex=x = ______ or x=x = ______\newline
Get tutor helpright-arrow

Posted 5 months ago

View all (179)

Related topics

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