Solve x^2+2*5x-187*5=0

$$x ^ { 2 } + 2 \cdot 5 x - 187 \cdot 5 = 0$$

Solve for x

$$x=8\sqrt{15}-5\approx 25.98386677$$

$$x=-8\sqrt{15}-5\approx -35.98386677$$

Steps Using the Quadratic Formula

Multiply 2 and 5 to get 10.

$$x^{2}+10x-187\times 5=0$$

Multiply 187 and 5 to get 935.

$$x^{2}+10x-935=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 10 for b, and -935 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-10±\sqrt{10^{2}-4\left(-935\right)}}{2}$$

Square 10.

$$x=\frac{-10±\sqrt{100-4\left(-935\right)}}{2}$$

Multiply -4 times -935.

$$x=\frac{-10±\sqrt{100+3740}}{2}$$

Add 100 to 3740.

$$x=\frac{-10±\sqrt{3840}}{2}$$

Take the square root of 3840.

$$x=\frac{-10±16\sqrt{15}}{2}$$

Now solve the equation x=\frac{-10±16\sqrt{15}}{2} when ± is plus. Add -10 to 16\sqrt{15}.

$$x=\frac{16\sqrt{15}-10}{2}$$

Divide -10+16\sqrt{15} by 2.

$$x=8\sqrt{15}-5$$

Now solve the equation x=\frac{-10±16\sqrt{15}}{2} when ± is minus. Subtract 16\sqrt{15} from -10.

$$x=\frac{-16\sqrt{15}-10}{2}$$

Divide -10-16\sqrt{15} by 2.

$$x=-8\sqrt{15}-5$$

The equation is now solved.

$$x=8\sqrt{15}-5 x=-8\sqrt{15}-5$$

Steps for Completing the Square

Multiply 2 and 5 to get 10.

$$x^{2}+10x-187\times 5=0$$

Multiply 187 and 5 to get 935.

$$x^{2}+10x-935=0$$

Add 935 to both sides. Anything plus zero gives itself.

$$x^{2}+10x=935$$

Divide 10, the coefficient of the x term, by 2 to get 5. Then add the square of 5 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+10x+5^{2}=935+5^{2}$$

Square 5.

$$x^{2}+10x+25=935+25$$

Add 935 to 25.

$$x^{2}+10x+25=960$$

Factor x^{2}+10x+25. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+5\right)^{2}=960$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+5\right)^{2}}=\sqrt{960}$$

Simplify.

$$x+5=8\sqrt{15} x+5=-8\sqrt{15}$$

Subtract 5 from both sides of the equation.

$$x=8\sqrt{15}-5 x=-8\sqrt{15}-5$$