Solve 95^2+w^2=120^2

$$95 ^ { 2 } + w ^ { 2 } = 120 ^ { 2 }$$

Solve for w

$$w=5\sqrt{215}\approx 73.314391493$$

$$w=-5\sqrt{215}\approx -73.314391493$$

Steps by Finding Square Root

Calculate 95 to the power of 2 and get 9025.

$$9025+w^{2}=120^{2}$$

Calculate 120 to the power of 2 and get 14400.

$$9025+w^{2}=14400$$

Subtract 9025 from both sides.

$$w^{2}=14400-9025$$

Subtract 9025 from 14400 to get 5375.

$$w^{2}=5375$$

Take the square root of both sides of the equation.

$$w=5\sqrt{215} w=-5\sqrt{215}$$

Steps Using the Quadratic Formula

Calculate 95 to the power of 2 and get 9025.

$$9025+w^{2}=120^{2}$$

Calculate 120 to the power of 2 and get 14400.

$$9025+w^{2}=14400$$

Subtract 14400 from both sides.

$$9025+w^{2}-14400=0$$

Subtract 14400 from 9025 to get -5375.

$$-5375+w^{2}=0$$

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.

$$w^{2}-5375=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -5375 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{0±\sqrt{0^{2}-4\left(-5375\right)}}{2}$$

Square 0.

$$w=\frac{0±\sqrt{-4\left(-5375\right)}}{2}$$

Multiply -4 times -5375.

$$w=\frac{0±\sqrt{21500}}{2}$$

Take the square root of 21500.

$$w=\frac{0±10\sqrt{215}}{2}$$

Now solve the equation w=\frac{0±10\sqrt{215}}{2} when ± is plus.

$$w=5\sqrt{215}$$

Now solve the equation w=\frac{0±10\sqrt{215}}{2} when ± is minus.

$$w=-5\sqrt{215}$$

The equation is now solved.

$$w=5\sqrt{215} w=-5\sqrt{215}$$