WordGPT

Solve -x² - 9x - 8 = 0

The solutions of -x² - 9x - 8 = 0 are x = -8 or x = -1.

x² +x += 0
−x2−9x−8=0⇒x=−8, −1-x^2 - 9x - 8 = 0 \Rightarrow x = -8,\ -1
Discriminant D = 49 · 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 - 9x - 8-10-8-6-4-2-25-20-15-10-551015x = -8x = -1vertexy = -x² - 9x - 8
Graph of y = -x² - 9x - 8. The curve crosses the x-axis at x = -8 and x = -1; the vertex is at (-4.5, 12.25).

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 = -9, c = -8.

    −x2−9x−8=0-x^2 - 9x - 8 = 0
  2. 2

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

    D=(−9)2−4⋅(−1)⋅(−8)=81−32=49D = (-9)^2 - 4\cdot(-1)\cdot(-8) = 81 - 32 = 49
  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=9±49−2x = \frac{-b \pm \sqrt{D}}{2a} = \frac{9 \pm \sqrt{49}}{-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) + (-9)·(-8) + (-8) = 0 ✓

LaTeX source of the formulas on this page
\[ -x^2 - 9x - 8 = 0\ \Rightarrow\ x = -8,\ -1 \]
\[ -x^2 - 9x - 8 = 0 \]
\[ D = (-9)^2 - 4\cdot(-1)\cdot(-8) = 81 - 32 = 49 \]
\[ -\left(x + 8\right)\left(x + 1\right) = 0 \]
\[ x + 8 = 0 \Rightarrow x = -8\qquad x + 1 = 0 \Rightarrow x = -1 \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{9 \pm \sqrt{49}}{-2} \]
\[ x = -8\quad\text{or}\quad x = -1 \]

The parabola y = -x² - 9x - 8

xy
-7.53.25
-6.58.25
-5.511.25
-4.512.25
-3.511.25
-2.58.25
-1.53.25

Questions

What are the solutions of -x² - 9x - 8 = 0?

The solutions of -x² - 9x - 8 = 0 are x = -8 or x = -1.

Does -x² - 9x - 8 = 0 factor?

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

What is the vertex of y = -x² - 9x - 8?

(-9/2, 49/4). The parabola opens downwards, so this is the maximum.

What are the sum and product of the roots?

Sum = −b/a = -9, product = c/a = 8.

Similar equations

    Solve -x² - 9x - 8 = 0: x = -8 or x = -1 (steps) | WordGPT