Solve x^2+0x-25=0

$$x ^ { 2 } + 0 x - 25 = 0$$

Solve for x

$$x=-5$$

$$x=5$$

Steps Using Difference of Squares

Consider x^{2}+0x-25. Rewrite x^{2}+0-25 as x^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-5\right)\left(x+5\right)=0$$

To find equation solutions, solve x-5=0 and x+5=0.

$$x=5 x=-5$$

Steps by Finding Square Root

Anything times zero gives zero.

$$x^{2}+0-25=0$$

Subtract 25 from 0 to get -25.

$$x^{2}-25=0$$

Add 25 to both sides. Anything plus zero gives itself.

$$x^{2}=25$$

Take the square root of both sides of the equation.

$$x=5 x=-5$$

Steps Using the Quadratic Formula

Anything times zero gives zero.

$$x^{2}+0-25=0$$

Subtract 25 from 0 to get -25.

$$x^{2}-25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-25\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-25\right)}}{2}$$

Multiply -4 times -25.

$$x=\frac{0±\sqrt{100}}{2}$$

Take the square root of 100.

$$x=\frac{0±10}{2}$$

Now solve the equation x=\frac{0±10}{2} when ± is plus. Divide 10 by 2.

$$x=5$$

Now solve the equation x=\frac{0±10}{2} when ± is minus. Divide -10 by 2.

$$x=-5$$

The equation is now solved.

$$x=5 x=-5$$

Steps Using Direct Factoring Method

Quadratic equations such as this one can be solved by a new direct factoring method that does not require guess work. To use the direct factoring method, the equation must be in the form x^2+Bx+C=0.

$$x ^ 2 +0x -25 = 0$$

Let r and s be the factors for the quadratic equation such that x^2+Bx+C=(x−r)(x−s) where sum of factors (r+s)=−B and the product of factors rs = C

$$r + s = 0 rs = -25$$

Two numbers r and s sum up to 0 exactly when the average of the two numbers is \frac{1}{2}*0 = 0. You can also see that the midpoint of r and s corresponds to the axis of symmetry of the parabola represented by the quadratic equation y=x^2+Bx+C. The values of r and s are equidistant from the center by an unknown quantity u. Express r and s with respect to variable u. <div style='padding: 8px'><img src='https://opalmath.azureedge.net/customsolver/quadraticgraph.png' style='width: 100%;max-width: 700px' /></div>

$$r = 0 - u s = 0 + u$$

To solve for unknown quantity u, substitute these in the product equation rs = -25

$$(0 - u) (0 + u) = -25$$

Simplify by expanding (a -b) (a + b) = a^2 – b^2

$$0 - u^2 = -25$$

Simplify the expression by subtracting 0 on both sides

$$-u^2 = -25-0 = -25$$

Simplify the expression by multiplying -1 on both sides and take the square root to obtain the value of unknown variable u

$$u^2 = 25 u = \pm\sqrt{25} = \pm 5$$

The factors r and s are the solutions to the quadratic equation. Substitute the value of u to compute the r and s.

$$r =0 - 5 = -5 s = 0 + 5 = 5$$