WordGPT

Solve 5x² + 5x = 0

The solutions of 5x² + 5x = 0 are x = 0 or x = -1.

x² +x += 0
5x2+5x=0⇒x=0, −15x^2 + 5x = 0 \Rightarrow x = 0,\ -1
Discriminant D = 25 · x ≈ 0, -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 = 5x² + 5x-3-2-11210203040x = 0x = -1vertexy = 5x² + 5x
Graph of y = 5x² + 5x. The curve crosses the x-axis at x = 0 and x = -1; the vertex is at (-0.5, -1.25).

How to work it out

  1. 1

    Write it in standard form a x² + b x + c = 0 and read off the coefficients: a = 5, b = 5, c = 0.

    5x2+5x=05x^2 + 5x = 0
  2. 2

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

    D=52−4⋅5⋅0=25+0=25D = 5^2 - 4\cdot5\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:

    5(x)(x+1)=05\left(x\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=0⇒x=0x+1=0⇒x=−1x = 0 \Rightarrow x = 0\qquad x + 1 = 0 \Rightarrow x = -1
  6. 6

    Method 2, The quadratic formula works for every quadratic:

    x=−b±D2a=−5±2510x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-5 \pm \sqrt{25}}{10}
  7. 7

    Simplify to get the solutions:

    x=0orx=−1x = 0\quad\text{or}\quad x = -1
  8. 8

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

LaTeX source of the formulas on this page
\[ 5x^2 + 5x = 0\ \Rightarrow\ x = 0,\ -1 \]
\[ 5x^2 + 5x = 0 \]
\[ D = 5^2 - 4\cdot5\cdot0 = 25 + 0 = 25 \]
\[ 5\left(x\right)\left(x + 1\right) = 0 \]
\[ x = 0 \Rightarrow x = 0\qquad x + 1 = 0 \Rightarrow x = -1 \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-5 \pm \sqrt{25}}{10} \]
\[ x = 0\quad\text{or}\quad x = -1 \]

The parabola y = 5x² + 5x

xy
-3.543.75
-2.518.75
-1.53.75
-0.5-1.25
0.53.75
1.518.75
2.543.75

Questions

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

The solutions of 5x² + 5x = 0 are x = 0 or x = -1.

Does 5x² + 5x = 0 factor?

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

What is the vertex of y = 5x² + 5x?

(-1/2, -5/4). The parabola opens upwards, so this is the minimum.

What are the sum and product of the roots?

Sum = −b/a = -1, product = c/a = 0.

Similar equations

    Solve 5x² + 5x = 0: x = 0 or x = -1 (steps) | WordGPT