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.\newlinez2+8z=21z^2 + 8z = 21\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinez=z = _____ or z=z = _____

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.\newlinez2+8z=21z^2 + 8z = 21\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinez=z = _____ or z=z = _____
  1. Rewrite equation as z2+bz=cz^2 + bz = c: Rewrite the equation in the form of z2+bz=cz^2 + bz = c.\newlineSubtract 2121 from both sides to set the equation to zero.\newlinez2+8z−21=0z^2 + 8z - 21 = 0
  2. Move constant term to right: Move the constant term to the right side of the equation. z2+8z=21z^2 + 8z = 21
  3. Complete the square: Complete the square by adding the square of half the coefficient of zz to both sides.\newlineSince (82)2=16(\frac{8}{2})^2 = 16, add 1616 to both sides.\newlinez2+8z+16=21+16z^2 + 8z + 16 = 21 + 16\newlinez2+8z+16=37z^2 + 8z + 16 = 37
  4. Factor left side: Factor the left side of the equation.\newline(z+4)2=37(z + 4)^2 = 37
  5. Take square root: Take the square root of both sides of the equation.\newline(z+4)2=±37\sqrt{(z + 4)^2} = \pm\sqrt{37}\newlinez+4=±37z + 4 = \pm\sqrt{37}
  6. Solve for z: Solve for z by isolating the variable.\newlineSubtract 44 from both sides of the equation.\newlinez+4−4=±37−4z + 4 - 4 = \pm\sqrt{37} - 4\newlinez=−4±37z = -4 \pm \sqrt{37}
  7. Calculate decimal values: Calculate the approximate decimal values of zz, rounded to the nearest hundredth.z≈−4+37z \approx -4 + \sqrt{37} implies z≈−4+6.08z \approx -4 + 6.08 which is z≈2.08z \approx 2.08.z≈−4−37z \approx -4 - \sqrt{37} implies z≈−4−6.08z \approx -4 - 6.08 which is z≈−10.08z \approx -10.08.

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 1 month 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 1 month 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 1 month 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 1 month 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 1 month 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 1 month 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 2 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 2 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 2 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 2 months ago

View all (180)