WordGPT

Solve x² - 10x = 0

The solutions of x² - 10x = 0 are x = 10 or x = 0.

x² +x += 0
x2−10x=0⇒x=10, 0x^2 - 10x = 0 \Rightarrow x = 10,\ 0
Discriminant D = 100 · x ≈ 10, 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 - 10x-224681012-30-20-10102030x = 10x = 0vertexy = x² - 10x
Graph of y = x² - 10x. The curve crosses the x-axis at x = 10 and x = 0; the vertex is at (5, -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 = -10, c = 0.

    x2−10x=0x^2 - 10x = 0
  2. 2

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

    D=(−10)2−4⋅1⋅0=100+0=100D = (-10)^2 - 4\cdot1\cdot0 = 100 + 0 = 100
  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−10)(x)=0\left(x - 10\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−10=0⇒x=10x=0⇒x=0x - 10 = 0 \Rightarrow x = 10\qquad x = 0 \Rightarrow x = 0
  6. 6

    Method 2, The quadratic formula works for every quadratic:

    x=−b±D2a=10±1002x = \frac{-b \pm \sqrt{D}}{2a} = \frac{10 \pm \sqrt{100}}{2}
  7. 7

    Simplify to get the solutions:

    x=10orx=0x = 10\quad\text{or}\quad x = 0
  8. 8

    Check by putting x = 10 back in: a·x² + b·x + c = 1·(100) + (-10)·(10) + 0 = 0 ✓

LaTeX source of the formulas on this page
\[ x^2 - 10x = 0\ \Rightarrow\ x = 10,\ 0 \]
\[ x^2 - 10x = 0 \]
\[ D = (-10)^2 - 4\cdot1\cdot0 = 100 + 0 = 100 \]
\[ \left(x - 10\right)\left(x\right) = 0 \]
\[ x - 10 = 0 \Rightarrow x = 10\qquad x = 0 \Rightarrow x = 0 \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{10 \pm \sqrt{100}}{2} \]
\[ x = 10\quad\text{or}\quad x = 0 \]

The parabola y = x² - 10x

xy
2-16
3-21
4-24
5-25
6-24
7-21
8-16

Questions

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

The solutions of x² - 10x = 0 are x = 10 or x = 0.

Does x² - 10x = 0 factor?

Yes: (x-10)(x) = 0.

What is the vertex of y = x² - 10x?

(5, -25). The parabola opens upwards, so this is the minimum.

What are the sum and product of the roots?

Sum = −b/a = 10, product = c/a = 0.

Similar equations

    Solve x² - 10x = 0: x = 10 or x = 0 (steps) | WordGPT