WordGPT

Solve -x² - 3x + 10 = 0

The solutions of -x² - 3x + 10 = 0 are x = -5 or x = 2.

x² +x += 0
−x2−3x+10=0⇒x=−5, 2-x^2 - 3x + 10 = 0 \Rightarrow x = -5,\ 2
Discriminant D = 49 · x ≈ -5, 2

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 - 3x + 10-6-4-224-25-20-15-10-551015x = -5x = 2vertexy = -x² - 3x + 10
Graph of y = -x² - 3x + 10. The curve crosses the x-axis at x = -5 and x = 2; the vertex is at (-1.5, 12.25).

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 = -3, c = 10.

    −x2−3x+10=0-x^2 - 3x + 10 = 0
  2. 2

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

    D=(−3)2−4⋅(−1)⋅10=9+40=49D = (-3)^2 - 4\cdot(-1)\cdot10 = 9 + 40 = 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+5)(x−2)=0-\left(x + 5\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+5=0⇒x=−5x−2=0⇒x=2x + 5 = 0 \Rightarrow x = -5\qquad x - 2 = 0 \Rightarrow x = 2
  6. 6

    Method 2, The quadratic formula works for every quadratic:

    x=−b±D2a=3±49−2x = \frac{-b \pm \sqrt{D}}{2a} = \frac{3 \pm \sqrt{49}}{-2}
  7. 7

    Simplify to get the solutions:

    x=−5orx=2x = -5\quad\text{or}\quad x = 2
  8. 8

    Check by putting x = -5 back in: a·x² + b·x + c = -1·(25) + (-3)·(-5) + 10 = 0 ✓

LaTeX source of the formulas on this page
\[ -x^2 - 3x + 10 = 0\ \Rightarrow\ x = -5,\ 2 \]
\[ -x^2 - 3x + 10 = 0 \]
\[ D = (-3)^2 - 4\cdot(-1)\cdot10 = 9 + 40 = 49 \]
\[ -\left(x + 5\right)\left(x - 2\right) = 0 \]
\[ x + 5 = 0 \Rightarrow x = -5\qquad x - 2 = 0 \Rightarrow x = 2 \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{3 \pm \sqrt{49}}{-2} \]
\[ x = -5\quad\text{or}\quad x = 2 \]

The parabola y = -x² - 3x + 10

xy
-4.53.25
-3.58.25
-2.511.25
-1.512.25
-0.511.25
0.58.25
1.53.25

Questions

What are the solutions of -x² - 3x + 10 = 0?

The solutions of -x² - 3x + 10 = 0 are x = -5 or x = 2.

Does -x² - 3x + 10 = 0 factor?

Yes: -1(x+5)(x-2) = 0.

What is the vertex of y = -x² - 3x + 10?

(-3/2, 49/4). The parabola opens downwards, so this is the maximum.

What are the sum and product of the roots?

Sum = −b/a = -3, product = c/a = -10.

Similar equations

    Solve -x² - 3x + 10 = 0: x = -5 or x = 2 (steps) | WordGPT