Solve 30^2+x^2=67^2

$$30 ^ { 2 } + x ^ { 2 } = 67 ^ { 2 }$$

Solve for x

$$x=\sqrt{3589}\approx 59.908263203$$

$$x=-\sqrt{3589}\approx -59.908263203$$

Steps by Finding Square Root

Calculate 30 to the power of 2 and get 900.

$$900+x^{2}=67^{2}$$

Calculate 67 to the power of 2 and get 4489.

$$900+x^{2}=4489$$

Subtract 900 from both sides.

$$x^{2}=4489-900$$

Subtract 900 from 4489 to get 3589.

$$x^{2}=3589$$

Take the square root of both sides of the equation.

$$x=\sqrt{3589} x=-\sqrt{3589}$$

Steps Using the Quadratic Formula

Calculate 30 to the power of 2 and get 900.

$$900+x^{2}=67^{2}$$

Calculate 67 to the power of 2 and get 4489.

$$900+x^{2}=4489$$

Subtract 4489 from both sides.

$$900+x^{2}-4489=0$$

Subtract 4489 from 900 to get -3589.

$$-3589+x^{2}=0$$

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.

$$x^{2}-3589=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -3589 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3589\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3589\right)}}{2}$$

Multiply -4 times -3589.

$$x=\frac{0±\sqrt{14356}}{2}$$

Take the square root of 14356.

$$x=\frac{0±2\sqrt{3589}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{3589}}{2} when ± is plus.

$$x=\sqrt{3589}$$

Now solve the equation x=\frac{0±2\sqrt{3589}}{2} when ± is minus.

$$x=-\sqrt{3589}$$

The equation is now solved.

$$x=\sqrt{3589} x=-\sqrt{3589}$$