Solve for x -7x+1-10x^2=0

$- 7 x + 1 - 10 x^{2} = 0$

Step 1

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 2

Substitute the values $a = - 10$ , $b = - 7$ , and $c = 1$ into the quadratic formula and solve for $x$ .

$\frac{7 \pm \sqrt{{(- 7)}^{2} - 4 \cdot (- 10 \cdot 1)}}{2 \cdot - 10}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 7$ to the power of $2$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot - 10 \cdot 1}}{2 \cdot - 10}$

Multiply $- 4 \cdot - 10 \cdot 1$ .

Multiply $- 4$ by $- 10$ .

$x = \frac{7 \pm \sqrt{49 + 40 \cdot 1}}{2 \cdot - 10}$

Multiply $40$ by $1$ .

$x = \frac{7 \pm \sqrt{49 + 40}}{2 \cdot - 10}$

Add $49$ and $40$ .

$x = \frac{7 \pm \sqrt{89}}{2 \cdot - 10}$

Multiply $2$ by $- 10$ .

$x = \frac{7 \pm \sqrt{89}}{- 20}$

Move the negative in front of the fraction.

$x = - \frac{7 \pm \sqrt{89}}{20}$

Step 4

The final answer is the combination of both solutions.

$x = - \frac{7 + \sqrt{89}}{20}, - \frac{7 - \sqrt{89}}{20}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{7 + \sqrt{89}}{20}, - \frac{7 - \sqrt{89}}{20}$

Decimal Form:

$x = - 0.82169905 \dots, 0.12169905 \dots$