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.\newline7g2−8g−9=07g^2 - 8g - 9 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineg=g = _____ or g=g = _____

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Solve a quadratic equation using the quadratic formularight chevron icon

Full solution

Q. Solve using the quadratic formula.\newline7g2−8g−9=07g^2 - 8g - 9 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineg=g = _____ or g=g = _____
  1. Identify values of aa, bb, cc: Identify the values of aa, bb, and cc in the quadratic equation 7g2−8g−9=07g^2 − 8g − 9 = 0. Compare 7g2−8g−9=07g^2 − 8g − 9 = 0 with the standard form ax2+bx+c=0ax^2 + bx + c = 0. a=7a = 7 bb00 bb11
  2. Substitute values into quadratic formula: Substitute the values of aa, bb, and cc into the quadratic formula g=−b±b2−4ac2ag = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substitute a=7a = 7, b=−8b = -8, and c=−9c = -9 into the formula. g=−(−8)±(−8)2−4⋅7⋅(−9)2⋅7g = \frac{-(-8) \pm \sqrt{(-8)^2 - 4\cdot7\cdot(-9)}}{2\cdot7} g=8±64+25214g = \frac{8 \pm \sqrt{64 + 252}}{14}
  3. Simplify expression and calculate discriminant: Simplify the expression under the square root and calculate the discriminant.64+252\sqrt{64 + 252} = 316\sqrt{316}
  4. Continue with quadratic formula: Continue with the quadratic formula using the simplified discriminant.\newlineg=8±31614g = \frac{8 \pm \sqrt{316}}{14}\newlineCalculate the two possible solutions for gg.\newlineg=8+31614g = \frac{8 + \sqrt{316}}{14} or g=8−31614g = \frac{8 - \sqrt{316}}{14}
  5. Simplify solutions and round: Simplify the solutions and, if necessary, round to the nearest hundredth.\newlineg=8+31614g = \frac{8 + \sqrt{316}}{14} or g=8−31614g = \frac{8 - \sqrt{316}}{14}\newlineg≈8+17.7814g \approx \frac{8 + 17.78}{14} or g≈8−17.7814g \approx \frac{8 - 17.78}{14}\newlineg≈25.7814g \approx \frac{25.78}{14} or g≈−9.7814g \approx \frac{-9.78}{14}\newlineg≈1.84g \approx 1.84 or g≈−0.70g \approx -0.70

More problems from Solve a quadratic equation using the quadratic formula

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 (110)