Solve 16x^2-8009+1000=0

$$16 x ^ { 2 } - 8009 + 1000 = 0$$

Solve for x

$$x = \frac{\sqrt{7009}}{4} \approx 20.929942666$$

$$x = -\frac{\sqrt{7009}}{4} \approx -20.929942666$$

Steps by Finding Square Root

Add -8009 and 1000 to get -7009.

$$16x^{2}-7009=0$$

Add 7009 to both sides. Anything plus zero gives itself.

$$16x^{2}=7009$$

Divide both sides by 16.

$$x^{2}=\frac{7009}{16}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{7009}}{4} x=-\frac{\sqrt{7009}}{4}$$

Steps Using the Quadratic Formula

Add -8009 and 1000 to get -7009.

$$16x^{2}-7009=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 16 for a, 0 for b, and -7009 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 16\left(-7009\right)}}{2\times 16}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 16\left(-7009\right)}}{2\times 16}$$

Multiply -4 times 16.

$$x=\frac{0±\sqrt{-64\left(-7009\right)}}{2\times 16}$$

Multiply -64 times -7009.

$$x=\frac{0±\sqrt{448576}}{2\times 16}$$

Take the square root of 448576.

$$x=\frac{0±8\sqrt{7009}}{2\times 16}$$

Multiply 2 times 16.

$$x=\frac{0±8\sqrt{7009}}{32}$$

Now solve the equation x=\frac{0±8\sqrt{7009}}{32} when ± is plus.

$$x=\frac{\sqrt{7009}}{4}$$

Now solve the equation x=\frac{0±8\sqrt{7009}}{32} when ± is minus.

$$x=-\frac{\sqrt{7009}}{4}$$

The equation is now solved.

$$x=\frac{\sqrt{7009}}{4} x=-\frac{\sqrt{7009}}{4}$$