Solve x^2=9.5^2+4^2

$$x ^ { 2 } = 9.5 ^ { 2 } + 4 ^ { 2 }$$

Solve for x

$$x = \frac{5 \sqrt{17}}{2} \approx 10.307764064$$

$$x = -\frac{5 \sqrt{17}}{2} \approx -10.307764064$$

Steps by Finding Square Root

Calculate 9.5 to the power of 2 and get 90.25.

$$x^{2}=90.25+4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$x^{2}=90.25+16$$

Add 90.25 and 16 to get 106.25.

$$x^{2}=106.25$$

Take the square root of both sides of the equation.

$$x=\frac{5\sqrt{17}}{2} x=-\frac{5\sqrt{17}}{2}$$

Steps Using the Quadratic Formula

Calculate 9.5 to the power of 2 and get 90.25.

$$x^{2}=90.25+4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$x^{2}=90.25+16$$

Add 90.25 and 16 to get 106.25.

$$x^{2}=106.25$$

Subtract 106.25 from both sides.

$$x^{2}-106.25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -106.25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-106.25\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-106.25\right)}}{2}$$

Multiply -4 times -106.25.

$$x=\frac{0±\sqrt{425}}{2}$$

Take the square root of 425.

$$x=\frac{0±5\sqrt{17}}{2}$$

Now solve the equation x=\frac{0±5\sqrt{17}}{2} when ± is plus.

$$x=\frac{5\sqrt{17}}{2}$$

Now solve the equation x=\frac{0±5\sqrt{17}}{2} when ± is minus.

$$x=-\frac{5\sqrt{17}}{2}$$

The equation is now solved.

$$x=\frac{5\sqrt{17}}{2} x=-\frac{5\sqrt{17}}{2}$$