WordGPT

Solve -2x² - 12x - 10 = 0

The solutions of -2x² - 12x - 10 = 0 are x = -5 or x = -1.

x² +x += 0
−2x2−12x−10=0⇒x=−5, −1-2x^2 - 12x - 10 = 0 \Rightarrow x = -5,\ -1
Discriminant D = 64 · x ≈ -5, -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 = -2x² - 12x - 10-7-6-5-4-3-2-11-30-20-1010x = -5x = -1vertexy = -2x² - 12x - 10
Graph of y = -2x² - 12x - 10. The curve crosses the x-axis at x = -5 and x = -1; the vertex is at (-3, 8).

How to work it out

  1. 1

    Write it in standard form a x² + b x + c = 0 and read off the coefficients: a = -2, b = -12, c = -10.

    −2x2−12x−10=0-2x^2 - 12x - 10 = 0
  2. 2

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

    D=(−12)2−4⋅(−2)⋅(−10)=144−80=64D = (-12)^2 - 4\cdot(-2)\cdot(-10) = 144 - 80 = 64
  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:

    −2(x+5)(x+1)=0-2\left(x + 5\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+5=0⇒x=−5x+1=0⇒x=−1x + 5 = 0 \Rightarrow x = -5\qquad x + 1 = 0 \Rightarrow x = -1
  6. 6

    Method 2, The quadratic formula works for every quadratic:

    x=−b±D2a=12±64−4x = \frac{-b \pm \sqrt{D}}{2a} = \frac{12 \pm \sqrt{64}}{-4}
  7. 7

    Simplify to get the solutions:

    x=−5orx=−1x = -5\quad\text{or}\quad x = -1
  8. 8

    Check by putting x = -5 back in: a·x² + b·x + c = -2·(25) + (-12)·(-5) + (-10) = 0 ✓

LaTeX source of the formulas on this page
\[ -2x^2 - 12x - 10 = 0\ \Rightarrow\ x = -5,\ -1 \]
\[ -2x^2 - 12x - 10 = 0 \]
\[ D = (-12)^2 - 4\cdot(-2)\cdot(-10) = 144 - 80 = 64 \]
\[ -2\left(x + 5\right)\left(x + 1\right) = 0 \]
\[ x + 5 = 0 \Rightarrow x = -5\qquad x + 1 = 0 \Rightarrow x = -1 \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{12 \pm \sqrt{64}}{-4} \]
\[ x = -5\quad\text{or}\quad x = -1 \]

The parabola y = -2x² - 12x - 10

xy
-6-10
-50
-46
-38
-26
-10
0-10

Questions

What are the solutions of -2x² - 12x - 10 = 0?

The solutions of -2x² - 12x - 10 = 0 are x = -5 or x = -1.

Does -2x² - 12x - 10 = 0 factor?

Yes: -2(x+5)(x+1) = 0.

What is the vertex of y = -2x² - 12x - 10?

(-3, 8). The parabola opens downwards, so this is the maximum.

What are the sum and product of the roots?

Sum = −b/a = -6, product = c/a = 5.

Similar equations

    Solve -2x² - 12x - 10 = 0: x = -5 or x = -1 (steps) | WordGPT