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Solve 4x² + 4x - 8 = 0

The solutions of 4x² + 4x - 8 = 0 are x = 1 or x = -2.

x² +x += 0
4x2+4x−8=0⇒x=1, −24x^2 + 4x - 8 = 0 \Rightarrow x = 1,\ -2
Discriminant D = 144 · x ≈ 1, -2

Change a, b or c (whole numbers, a not 0) and the exact solutions follow.

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Graph of y = 4x² + 4x - 8-4-3-2-1123-10102030405060x = 1x = -2vertexy = 4x² + 4x - 8
Graph of y = 4x² + 4x - 8. The curve crosses the x-axis at x = 1 and x = -2; the vertex is at (-0.5, -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 = 4, b = 4, c = -8.

    4x2+4x−8=04x^2 + 4x - 8 = 0
  2. 2

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

    D=42−4⋅4⋅(−8)=16+128=144D = 4^2 - 4\cdot4\cdot(-8) = 16 + 128 = 144
  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:

    4(x−1)(x+2)=04\left(x - 1\right)\left(x + 2\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−1=0⇒x=1x+2=0⇒x=−2x - 1 = 0 \Rightarrow x = 1\qquad x + 2 = 0 \Rightarrow x = -2
  6. 6

    Method 2, The quadratic formula works for every quadratic:

    x=−b±D2a=−4±1448x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-4 \pm \sqrt{144}}{8}
  7. 7

    Simplify to get the solutions:

    x=1orx=−2x = 1\quad\text{or}\quad x = -2
  8. 8

    Check by putting x = 1 back in: a·x² + b·x + c = 4·(1) + 4·(1) + (-8) = 0 ✓

LaTeX source of the formulas on this page
\[ 4x^2 + 4x - 8 = 0\ \Rightarrow\ x = 1,\ -2 \]
\[ 4x^2 + 4x - 8 = 0 \]
\[ D = 4^2 - 4\cdot4\cdot(-8) = 16 + 128 = 144 \]
\[ 4\left(x - 1\right)\left(x + 2\right) = 0 \]
\[ x - 1 = 0 \Rightarrow x = 1\qquad x + 2 = 0 \Rightarrow x = -2 \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-4 \pm \sqrt{144}}{8} \]
\[ x = 1\quad\text{or}\quad x = -2 \]

The parabola y = 4x² + 4x - 8

xy
-3.527
-2.57
-1.5-5
-0.5-9
0.5-5
1.57
2.527

Questions

What are the solutions of 4x² + 4x - 8 = 0?

The solutions of 4x² + 4x - 8 = 0 are x = 1 or x = -2.

Does 4x² + 4x - 8 = 0 factor?

Yes: 4(x-1)(x+2) = 0.

What is the vertex of y = 4x² + 4x - 8?

(-1/2, -9). 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 = -2.

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