WordGPT

Solve x² - 5x = 0

The solutions of x² - 5x = 0 are x = 5 or x = 0.

x² +x += 0
x2−5x=0⇒x=5, 0x^2 - 5x = 0 \Rightarrow x = 5,\ 0
Discriminant D = 25 · x ≈ 5, 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 - 5x-2-11234567-55101520x = 5x = 0vertexy = x² - 5x
Graph of y = x² - 5x. The curve crosses the x-axis at x = 5 and x = 0; the vertex is at (2.5, -6.25).

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 = -5, c = 0.

    x2−5x=0x^2 - 5x = 0
  2. 2

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

    D=(−5)2−4⋅1⋅0=25+0=25D = (-5)^2 - 4\cdot1\cdot0 = 25 + 0 = 25
  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−5)(x)=0\left(x - 5\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−5=0⇒x=5x=0⇒x=0x - 5 = 0 \Rightarrow x = 5\qquad x = 0 \Rightarrow x = 0
  6. 6

    Method 2, The quadratic formula works for every quadratic:

    x=−b±D2a=5±252x = \frac{-b \pm \sqrt{D}}{2a} = \frac{5 \pm \sqrt{25}}{2}
  7. 7

    Simplify to get the solutions:

    x=5orx=0x = 5\quad\text{or}\quad x = 0
  8. 8

    Check by putting x = 5 back in: a·x² + b·x + c = 1·(25) + (-5)·(5) + 0 = 0 ✓

LaTeX source of the formulas on this page
\[ x^2 - 5x = 0\ \Rightarrow\ x = 5,\ 0 \]
\[ x^2 - 5x = 0 \]
\[ D = (-5)^2 - 4\cdot1\cdot0 = 25 + 0 = 25 \]
\[ \left(x - 5\right)\left(x\right) = 0 \]
\[ x - 5 = 0 \Rightarrow x = 5\qquad x = 0 \Rightarrow x = 0 \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{5 \pm \sqrt{25}}{2} \]
\[ x = 5\quad\text{or}\quad x = 0 \]

The parabola y = x² - 5x

xy
-0.52.75
0.5-2.25
1.5-5.25
2.5-6.25
3.5-5.25
4.5-2.25
5.52.75

Questions

What are the solutions of x² - 5x = 0?

The solutions of x² - 5x = 0 are x = 5 or x = 0.

Does x² - 5x = 0 factor?

Yes: (x-5)(x) = 0.

What is the vertex of y = x² - 5x?

(5/2, -25/4). The parabola opens upwards, so this is the minimum.

What are the sum and product of the roots?

Sum = −b/a = 5, product = c/a = 0.

Similar equations

    Solve x² - 5x = 0: x = 5 or x = 0 (steps) | WordGPT