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Solve 2x² + 11x - 10 = 0

The solutions of 2x² + 11x - 10 = 0 are x = (-11 + √201)/4 or x = (-11 - √201)/4, that is x ≈ 0.79436172 and x ≈ -6.2943617.

x² +x += 0
2x2+11x−10=0⇒x=−11+2014, −11−20142x^2 + 11x - 10 = 0 \Rightarrow x = \frac{-11 + \sqrt{201}}{4},\ \frac{-11 - \sqrt{201}}{4}
Discriminant D = 201 · x ≈ 0.794362, -6.29436

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

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Graph of y = 2x² + 11x - 10-8-6-4-22-30-20-101020304050x = 0.79436172x = -6.2943617vertexy = 2x² + 11x - 10
Graph of y = 2x² + 11x - 10. The curve crosses the x-axis at x = 0.79436172 and x = -6.2943617; the vertex is at (-2.75, -25.125).

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 = 11, c = -10.

    2x2+11x−10=02x^2 + 11x - 10 = 0
  2. 2

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

    D=112−4⋅2⋅(−10)=121+80=201D = 11^2 - 4\cdot2\cdot(-10) = 121 + 80 = 201
  3. 3

    D is positive, so there are two different real solutions.

  4. 4

    The quadratic formula works for every quadratic:

    x=−b±D2a=−11±2014x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-11 \pm \sqrt{201}}{4}
  5. 5

    Simplify (pull the square out of the root) to get the solutions:

    x=−11+2014orx=−11−2014x = \frac{-11 + \sqrt{201}}{4}\quad\text{or}\quad x = \frac{-11 - \sqrt{201}}{4}
  6. 6

    As decimals: x ≈ 0.79436172 and x ≈ -6.2943617.

  7. 7

    Check numerically: for x ≈ 0.79436172 the left side is 0 (zero up to rounding) ✓

LaTeX source of the formulas on this page
\[ 2x^2 + 11x - 10 = 0\ \Rightarrow\ x = \frac{-11 + \sqrt{201}}{4},\ \frac{-11 - \sqrt{201}}{4} \]
\[ 2x^2 + 11x - 10 = 0 \]
\[ D = 11^2 - 4\cdot2\cdot(-10) = 121 + 80 = 201 \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-11 \pm \sqrt{201}}{4} \]
\[ x = \frac{-11 + \sqrt{201}}{4}\quad\text{or}\quad x = \frac{-11 - \sqrt{201}}{4} \]

The parabola y = 2x² + 11x - 10

xy
-5.75-7.125
-4.75-17.125
-3.75-23.125
-2.75-25.125
-1.75-23.125
-0.75-17.125
0.25-7.125

Questions

What are the solutions of 2x² + 11x - 10 = 0?

The solutions of 2x² + 11x - 10 = 0 are x = (-11 + √201)/4 or x = (-11 - √201)/4, that is x ≈ 0.79436172 and x ≈ -6.2943617.

Does 2x² + 11x - 10 = 0 factor?

Not over the integers, because the discriminant 201 is not a perfect square. Use the quadratic formula.

What is the vertex of y = 2x² + 11x - 10?

(-11/4, -201/8). The parabola opens upwards, so this is the minimum.

What are the sum and product of the roots?

Sum = −b/a = -11/2, product = c/a = -5.

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    Solve 2x² + 11x - 10 = 0: x = (-11 + √201)/4 or x = (-11 - √201)/4 (steps) | WordGPT