Solve x^2+(2.5^2)=7^2

$${ x }^{ 2 } +( { 2.5 }^{ 2 } )= { 7 }^{ 2 }$$

Solve for x

$$x = \frac{3 \sqrt{19}}{2} \approx 6.538348415$$

$$x = -\frac{3 \sqrt{19}}{2} \approx -6.538348415$$

Steps by Finding Square Root

Calculate 2.5 to the power of 2 and get 6.25.

$$x^{2}+6.25=7^{2}$$

Calculate 7 to the power of 2 and get 49.

$$x^{2}+6.25=49$$

Subtract 6.25 from both sides.

$$x^{2}=49-6.25$$

Subtract 6.25 from 49 to get 42.75.

$$x^{2}=42.75$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{19}}{2} x=-\frac{3\sqrt{19}}{2}$$

Steps Using the Quadratic Formula

Calculate 2.5 to the power of 2 and get 6.25.

$$x^{2}+6.25=7^{2}$$

Calculate 7 to the power of 2 and get 49.

$$x^{2}+6.25=49$$

Subtract 49 from both sides.

$$x^{2}+6.25-49=0$$

Subtract 49 from 6.25 to get -42.75.

$$x^{2}-42.75=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -42.75 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-42.75\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-42.75\right)}}{2}$$

Multiply -4 times -42.75.

$$x=\frac{0±\sqrt{171}}{2}$$

Take the square root of 171.

$$x=\frac{0±3\sqrt{19}}{2}$$

Now solve the equation x=\frac{0±3\sqrt{19}}{2} when ± is plus.

$$x=\frac{3\sqrt{19}}{2}$$

Now solve the equation x=\frac{0±3\sqrt{19}}{2} when ± is minus.

$$x=-\frac{3\sqrt{19}}{2}$$

The equation is now solved.

$$x=\frac{3\sqrt{19}}{2} x=-\frac{3\sqrt{19}}{2}$$