Solve 3.7^2+x^2=6.3^2

$${ 3.7 }^{ 2 } + { x }^{ 2 } = { 6.3 }^{ 2 }$$

Solve for x

$$x=\sqrt{26}\approx 5.099019514$$

$$x=-\sqrt{26}\approx -5.099019514$$

Steps by Finding Square Root

Calculate 3.7 to the power of 2 and get 13.69.

$$13.69+x^{2}=6.3^{2}$$

Calculate 6.3 to the power of 2 and get 39.69.

$$13.69+x^{2}=39.69$$

Subtract 13.69 from both sides.

$$x^{2}=39.69-13.69$$

Subtract 13.69 from 39.69 to get 26.

$$x^{2}=26$$

Take the square root of both sides of the equation.

$$x=\sqrt{26} x=-\sqrt{26}$$

Steps Using the Quadratic Formula

Calculate 3.7 to the power of 2 and get 13.69.

$$13.69+x^{2}=6.3^{2}$$

Calculate 6.3 to the power of 2 and get 39.69.

$$13.69+x^{2}=39.69$$

Subtract 39.69 from both sides.

$$13.69+x^{2}-39.69=0$$

Subtract 39.69 from 13.69 to get -26.

$$-26+x^{2}=0$$

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.

$$x^{2}-26=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -26 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-26\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-26\right)}}{2}$$

Multiply -4 times -26.

$$x=\frac{0±\sqrt{104}}{2}$$

Take the square root of 104.

$$x=\frac{0±2\sqrt{26}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{26}}{2} when ± is plus.

$$x=\sqrt{26}$$

Now solve the equation x=\frac{0±2\sqrt{26}}{2} when ± is minus.

$$x=-\sqrt{26}$$

The equation is now solved.

$$x=\sqrt{26} x=-\sqrt{26}$$