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 for ff.\newlinef2+12f−13=0f^2 + 12f - 13 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinef=f = ____

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Solve a quadratic equation by factoringright chevron icon

Full solution

Q. Solve for ff.\newlinef2+12f−13=0f^2 + 12f - 13 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinef=f = ____
  1. Identify the quadratic equation: Identify the quadratic equation.\newlineThe given equation is f2+12f−13=0f^2 + 12f - 13 = 0, which is a quadratic equation in the standard form af2+bf+c=0af^2 + bf + c = 0, where a=1a = 1, b=12b = 12, and c=−13c = -13.
  2. Use the quadratic formula: Use the quadratic formula to solve for ff. The quadratic formula is f=−b±b2−4ac2af = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. For our equation, a=1a = 1, b=12b = 12, and c=−13c = -13.
  3. Calculate the discriminant: Calculate the discriminant.\newlineThe discriminant is the part of the quadratic formula under the square root: b2−4acb^2 - 4ac. Let's calculate it:\newlineDiscriminant = (12)2−4(1)(−13)=144+52=196(12)^2 - 4(1)(-13) = 144 + 52 = 196.
  4. Two real solutions: Since the discriminant is positive, there are two real solutions.\newlineNow we can find the two solutions using the quadratic formula:\newlinef=−12±1962×1f = \frac{-12 \pm \sqrt{196}}{2 \times 1}.
  5. Calculate the two solutions: Calculate the two solutions.\newlineFirst solution:\newlinef=−12+1962=−12+142=22=1f = \frac{-12 + \sqrt{196}}{2} = \frac{-12 + 14}{2} = \frac{2}{2} = 1.\newlineSecond solution:\newlinef=−12−1962=−12−142=−262=−13f = \frac{-12 - \sqrt{196}}{2} = \frac{-12 - 14}{2} = \frac{-26}{2} = -13.

More problems from Solve a quadratic equation by factoring

Question
The function h(t)=−16t2+144h(t) = -16t^{2} + 144 represents the height, h(t)h(t), in feet, of an object from the ground at tt seconds after it is dropped. A realistic domain (for time) for this function is:\newline(A)(A) −3≤t≤3-3 \leq t \leq 3\newline(B)(B) 0≤t≤30 \leq t \leq 3\newline(C)(C) 0≤h≤1440 \leq h \leq 144\newline(D)(D) all real numbers
Get tutor helpright-arrow

Posted 8 months ago

Question
Деление с остатком
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve the system of equations.\newliney=x2+40x−20y = x^2 + 40x - 20\newliney=40x−4y = 40x - 4\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve the system of equations.\newliney=−36x+26y = -36x + 26\newliney=x2−46x−13y = x^2 - 46x - 13\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve the system of equations.\newliney=32x2+32x−23y = 32x^2 + 32x - 23\newliney=32x+9y = 32x + 9\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve the system of equations.\newliney=x2+12x−41y = x^2 + 12x - 41\newliney=17x+9y = 17x + 9\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve the system of equations.\newliney=x2−43x−14y = x^2 - 43x - 14\newliney=−45x+34y = -45x + 34\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve the system of equations.\newliney=14x−26y = 14x - 26\newliney=2x2+14x−34y = 2x^2 + 14x - 34\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 8 months ago

Question
Find the discriminant.\newline3u2−8u+4=03u^2 - 8u + 4 = 0
Get tutor helpright-arrow

Posted 8 months ago

Question
Find the discriminant.\newline7w2+5w+8=07w^2 + 5w + 8 = 0
Get tutor helpright-arrow

Posted 8 months ago

View all (6)

Related topics

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