WordGPT

Solve x² - 7x - 8 = 0

The solutions of x² - 7x - 8 = 0 are x = 8 or x = -1.

x² +x += 0
x2−7x−8=0⇒x=8, −1x^2 - 7x - 8 = 0 \Rightarrow x = 8,\ -1
Discriminant D = 81 · x ≈ 8, -1

Change a, b or c (whole numbers, a not 0) and the exact solutions follow.

Explain it step by step in chatMake a short video of it
Graph of y = x² - 7x - 8-2246810-20-10102030x = 8x = -1vertexy = x² - 7x - 8
Graph of y = x² - 7x - 8. The curve crosses the x-axis at x = 8 and x = -1; the vertex is at (3.5, -20.25).

How to work it out

  1. 1

    Write it in standard form a x² + b x + c = 0 and read off the coefficients: a = 1, b = -7, c = -8.

    x2−7x−8=0x^2 - 7x - 8 = 0
  2. 2

    Work out the discriminant D = b² − 4ac. Its sign tells you how many real solutions there are.

    D=(−7)2−4⋅1⋅(−8)=49+32=81D = (-7)^2 - 4\cdot1\cdot(-8) = 49 + 32 = 81
  3. 3

    D is positive, so there are two different real solutions.

  4. 4

    Method 1, factoring. The roots are rational, so the left side factors:

    (x−8)(x+1)=0\left(x - 8\right)\left(x + 1\right) = 0
  5. 5

    A product is zero when one of its factors is zero, so set each factor equal to 0 and solve:

    x−8=0⇒x=8x+1=0⇒x=−1x - 8 = 0 \Rightarrow x = 8\qquad x + 1 = 0 \Rightarrow x = -1
  6. 6

    Method 2, The quadratic formula works for every quadratic:

    x=−b±D2a=7±812x = \frac{-b \pm \sqrt{D}}{2a} = \frac{7 \pm \sqrt{81}}{2}
  7. 7

    Simplify to get the solutions:

    x=8orx=−1x = 8\quad\text{or}\quad x = -1
  8. 8

    Check by putting x = 8 back in: a·x² + b·x + c = 1·(64) + (-7)·(8) + (-8) = 0 ✓

LaTeX source of the formulas on this page
\[ x^2 - 7x - 8 = 0\ \Rightarrow\ x = 8,\ -1 \]
\[ x^2 - 7x - 8 = 0 \]
\[ D = (-7)^2 - 4\cdot1\cdot(-8) = 49 + 32 = 81 \]
\[ \left(x - 8\right)\left(x + 1\right) = 0 \]
\[ x - 8 = 0 \Rightarrow x = 8\qquad x + 1 = 0 \Rightarrow x = -1 \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{7 \pm \sqrt{81}}{2} \]
\[ x = 8\quad\text{or}\quad x = -1 \]

The parabola y = x² - 7x - 8

xy
0.5-11.25
1.5-16.25
2.5-19.25
3.5-20.25
4.5-19.25
5.5-16.25
6.5-11.25

Questions

What are the solutions of x² - 7x - 8 = 0?

The solutions of x² - 7x - 8 = 0 are x = 8 or x = -1.

Does x² - 7x - 8 = 0 factor?

Yes: (x-8)(x+1) = 0.

What is the vertex of y = x² - 7x - 8?

(7/2, -81/4). The parabola opens upwards, so this is the minimum.

What are the sum and product of the roots?

Sum = −b/a = 7, product = c/a = -8.

Similar equations

    Solve x² - 7x - 8 = 0: x = 8 or x = -1 (steps) | WordGPT