WordGPT

Solve -x² - 6x = 0

The solutions of -x² - 6x = 0 are x = -6 or x = 0.

x² +x += 0
−x2−6x=0⇒x=−6, 0-x^2 - 6x = 0 \Rightarrow x = -6,\ 0
Discriminant D = 36 · x ≈ -6, 0

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 - 6x-8-6-4-22-20-15-10-5510x = -6x = 0vertexy = -x² - 6x
Graph of y = -x² - 6x. The curve crosses the x-axis at x = -6 and x = 0; the vertex is at (-3, 9).

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 = -6, c = 0.

    −x2−6x=0-x^2 - 6x = 0
  2. 2

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

    D=(−6)2−4⋅(−1)⋅0=36+0=36D = (-6)^2 - 4\cdot(-1)\cdot0 = 36 + 0 = 36
  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+6)(x)=0-\left(x + 6\right)\left(x\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+6=0⇒x=−6x=0⇒x=0x + 6 = 0 \Rightarrow x = -6\qquad x = 0 \Rightarrow x = 0
  6. 6

    Method 2, The quadratic formula works for every quadratic:

    x=−b±D2a=6±36−2x = \frac{-b \pm \sqrt{D}}{2a} = \frac{6 \pm \sqrt{36}}{-2}
  7. 7

    Simplify to get the solutions:

    x=−6orx=0x = -6\quad\text{or}\quad x = 0
  8. 8

    Check by putting x = -6 back in: a·x² + b·x + c = -1·(36) + (-6)·(-6) + 0 = 0 ✓

LaTeX source of the formulas on this page
\[ -x^2 - 6x = 0\ \Rightarrow\ x = -6,\ 0 \]
\[ -x^2 - 6x = 0 \]
\[ D = (-6)^2 - 4\cdot(-1)\cdot0 = 36 + 0 = 36 \]
\[ -\left(x + 6\right)\left(x\right) = 0 \]
\[ x + 6 = 0 \Rightarrow x = -6\qquad x = 0 \Rightarrow x = 0 \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{6 \pm \sqrt{36}}{-2} \]
\[ x = -6\quad\text{or}\quad x = 0 \]

The parabola y = -x² - 6x

xy
-60
-55
-48
-39
-28
-15
00

Questions

What are the solutions of -x² - 6x = 0?

The solutions of -x² - 6x = 0 are x = -6 or x = 0.

Does -x² - 6x = 0 factor?

Yes: -1(x+6)(x) = 0.

What is the vertex of y = -x² - 6x?

(-3, 9). 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 = 0.

Similar equations

    Solve -x² - 6x = 0: x = -6 or x = 0 (steps) | WordGPT