Solve 3^2=2.5^2+x^2

$${ 3 }^{ 2 } = { 2.5 }^{ 2 } + { x }^{ 2 }$$

Solve for x

$$x = \frac{\sqrt{11}}{2} \approx 1.658312395$$

$$x = -\frac{\sqrt{11}}{2} \approx -1.658312395$$

Steps by Finding Square Root

Calculate 3 to the power of 2 and get 9.

$$9=2.5^{2}+x^{2}$$

Calculate 2.5 to the power of 2 and get 6.25.

$$9=6.25+x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$6.25+x^{2}=9$$

Subtract 6.25 from both sides.

$$x^{2}=9-6.25$$

Subtract 6.25 from 9 to get 2.75.

$$x^{2}=2.75$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{11}}{2} x=-\frac{\sqrt{11}}{2}$$

Steps Using the Quadratic Formula

Calculate 3 to the power of 2 and get 9.

$$9=2.5^{2}+x^{2}$$

Calculate 2.5 to the power of 2 and get 6.25.

$$9=6.25+x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$6.25+x^{2}=9$$

Subtract 9 from both sides.

$$6.25+x^{2}-9=0$$

Subtract 9 from 6.25 to get -2.75.

$$-2.75+x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}-2.75=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -2.75 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2.75\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2.75\right)}}{2}$$

Multiply -4 times -2.75.

$$x=\frac{0±\sqrt{11}}{2}$$

Now solve the equation x=\frac{0±\sqrt{11}}{2} when ± is plus.

$$x=\frac{\sqrt{11}}{2}$$

Now solve the equation x=\frac{0±\sqrt{11}}{2} when ± is minus.

$$x=-\frac{\sqrt{11}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{11}}{2} x=-\frac{\sqrt{11}}{2}$$