WordGPT

Solve 2x² + 7x = 0

The solutions of 2x² + 7x = 0 are x = 0 or x = -7/2.

x² +x += 0
2x2+7x=0⇒x=0, −722x^2 + 7x = 0 \Rightarrow x = 0,\ -\frac{7}{2}
Discriminant D = 49 · x ≈ 0, -3.5

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 + 7x-6-5-4-3-2-112-10-551015202530x = 0x = -3.5vertexy = 2x² + 7x
Graph of y = 2x² + 7x. The curve crosses the x-axis at x = 0 and x = -3.5; the vertex is at (-1.75, -6.125).

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 = 7, c = 0.

    2x2+7x=02x^2 + 7x = 0
  2. 2

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

    D=72−4⋅2⋅0=49+0=49D = 7^2 - 4\cdot2\cdot0 = 49 + 0 = 49
  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)(2x+7)=0\left(x\right)\left(2x + 7\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=02x+7=0⇒x=−72x = 0 \Rightarrow x = 0\qquad 2x + 7 = 0 \Rightarrow x = -\frac{7}{2}
  6. 6

    Method 2, The quadratic formula works for every quadratic:

    x=−b±D2a=−7±494x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-7 \pm \sqrt{49}}{4}
  7. 7

    Simplify to get the solutions:

    x=0orx=−72x = 0\quad\text{or}\quad x = -\frac{7}{2}
  8. 8

    Check by putting x = 0 back in: a·x² + b·x + c = 2·(0) + 7·(0) + 0 = 0 ✓

LaTeX source of the formulas on this page
\[ 2x^2 + 7x = 0\ \Rightarrow\ x = 0,\ -\frac{7}{2} \]
\[ 2x^2 + 7x = 0 \]
\[ D = 7^2 - 4\cdot2\cdot0 = 49 + 0 = 49 \]
\[ \left(x\right)\left(2x + 7\right) = 0 \]
\[ x = 0 \Rightarrow x = 0\qquad 2x + 7 = 0 \Rightarrow x = -\frac{7}{2} \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-7 \pm \sqrt{49}}{4} \]
\[ x = 0\quad\text{or}\quad x = -\frac{7}{2} \]

The parabola y = 2x² + 7x

xy
-4.7511.875
-3.751.875
-2.75-4.125
-1.75-6.125
-0.75-4.125
0.251.875
1.2511.875

Questions

What are the solutions of 2x² + 7x = 0?

The solutions of 2x² + 7x = 0 are x = 0 or x = -7/2.

Does 2x² + 7x = 0 factor?

Yes: (x)(2x+7) = 0.

What is the vertex of y = 2x² + 7x?

(-7/4, -49/8). The parabola opens upwards, so this is the minimum.

What are the sum and product of the roots?

Sum = −b/a = -7/2, product = c/a = 0.

Similar equations

    Solve 2x² + 7x = 0: x = 0 or x = -7/2 (steps) | WordGPT