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.\newlines2+8s=15s^2 + 8s = 15\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlines=s = _____ or s=s = _____

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.\newlines2+8s=15s^2 + 8s = 15\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlines=s = _____ or s=s = _____
  1. Rewrite Equation: Rewrite the equation in the form of s2+bs=cs^2 + bs = c.\newlineSubtract 1515 from both sides to set the equation to zero.\newlines2+8s−15=0s^2 + 8s - 15 = 0
  2. Isolate Terms: Add 1515 to both sides to isolate the s2s^2 and ss terms on one side.\newlines2+8s=15s^2 + 8s = 15
  3. Complete the Square: To complete the square, add (82)2(\frac{8}{2})^2 to both sides of the equation.\newlineSince (82)2=16(\frac{8}{2})^2 = 16, add 1616 to both sides.\newlines2+8s+16=15+16s^2 + 8s + 16 = 15 + 16\newlines2+8s+16=31s^2 + 8s + 16 = 31
  4. Factor Equation: Factor the left side of the equation.\newline(s+4)2=31(s + 4)^2 = 31
  5. Take Square Root: Take the square root of both sides of the equation.\newline(s+4)2=±31\sqrt{(s + 4)^2} = \pm\sqrt{31}\newlines+4=±31s + 4 = \pm\sqrt{31}
  6. Solve for ss: Solve for ss by subtracting 44 from both sides of the equation.s+4−4=±31−4s + 4 - 4 = \pm\sqrt{31} - 4s=−4±31s = -4 \pm \sqrt{31}
  7. Calculate Approximate Values: Calculate the approximate decimal values of ss, rounded to the nearest hundredth.s≈−4+31s \approx -4 + \sqrt{31}s≈−4+5.57s \approx -4 + 5.57s≈1.57s \approx 1.57Ands≈−4−31s \approx -4 - \sqrt{31}s≈−4−5.57s \approx -4 - 5.57s≈−9.57s \approx -9.57

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