Solve x^2+25x*63=5

$${ x }^{ 2 } +25x \times 63=5$$

Solve for x

$$x=\frac{\sqrt{2480645}-1575}{2}\approx 0.003174597$$

$$x=\frac{-\sqrt{2480645}-1575}{2}\approx -1575.003174597$$

Steps Using the Quadratic Formula

Multiply 25 and 63 to get 1575.

$$x^{2}+1575x=5$$

Subtract 5 from both sides.

$$x^{2}+1575x-5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 1575 for b, and -5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1575±\sqrt{1575^{2}-4\left(-5\right)}}{2}$$

Square 1575.

$$x=\frac{-1575±\sqrt{2480625-4\left(-5\right)}}{2}$$

Multiply -4 times -5.

$$x=\frac{-1575±\sqrt{2480625+20}}{2}$$

Add 2480625 to 20.

$$x=\frac{-1575±\sqrt{2480645}}{2}$$

Now solve the equation x=\frac{-1575±\sqrt{2480645}}{2} when ± is plus. Add -1575 to \sqrt{2480645}.

$$x=\frac{\sqrt{2480645}-1575}{2}$$

Now solve the equation x=\frac{-1575±\sqrt{2480645}}{2} when ± is minus. Subtract \sqrt{2480645} from -1575.

$$x=\frac{-\sqrt{2480645}-1575}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{2480645}-1575}{2} x=\frac{-\sqrt{2480645}-1575}{2}$$

Steps for Completing the Square

Multiply 25 and 63 to get 1575.

$$x^{2}+1575x=5$$

Divide 1575, the coefficient of the x term, by 2 to get \frac{1575}{2}. Then add the square of \frac{1575}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+1575x+\left(\frac{1575}{2}\right)^{2}=5+\left(\frac{1575}{2}\right)^{2}$$

Square \frac{1575}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+1575x+\frac{2480625}{4}=5+\frac{2480625}{4}$$

Add 5 to \frac{2480625}{4}.

$$x^{2}+1575x+\frac{2480625}{4}=\frac{2480645}{4}$$

Factor x^{2}+1575x+\frac{2480625}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{1575}{2}\right)^{2}=\frac{2480645}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{1575}{2}\right)^{2}}=\sqrt{\frac{2480645}{4}}$$

Simplify.

$$x+\frac{1575}{2}=\frac{\sqrt{2480645}}{2} x+\frac{1575}{2}=-\frac{\sqrt{2480645}}{2}$$

Subtract \frac{1575}{2} from both sides of the equation.

$$x=\frac{\sqrt{2480645}-1575}{2} x=\frac{-\sqrt{2480645}-1575}{2}$$