Solve left(44-100right)^2+y^2=100^2

$${ \left(44-100 \right) }^{ 2 } + { y }^{ 2 } = { 100 }^{ 2 }$$

Solve for y

$$y=4\sqrt{429}\approx 82.849260709$$

$$y=-4\sqrt{429}\approx -82.849260709$$

Steps by Finding Square Root

Subtract 100 from 44 to get -56.

$$\left(-56\right)^{2}+y^{2}=100^{2}$$

Calculate -56 to the power of 2 and get 3136.

$$3136+y^{2}=100^{2}$$

Calculate 100 to the power of 2 and get 10000.

$$3136+y^{2}=10000$$

Subtract 3136 from both sides.

$$y^{2}=10000-3136$$

Subtract 3136 from 10000 to get 6864.

$$y^{2}=6864$$

Take the square root of both sides of the equation.

$$y=4\sqrt{429} y=-4\sqrt{429}$$

Steps Using the Quadratic Formula

Subtract 100 from 44 to get -56.

$$\left(-56\right)^{2}+y^{2}=100^{2}$$

Calculate -56 to the power of 2 and get 3136.

$$3136+y^{2}=100^{2}$$

Calculate 100 to the power of 2 and get 10000.

$$3136+y^{2}=10000$$

Subtract 10000 from both sides.

$$3136+y^{2}-10000=0$$

Subtract 10000 from 3136 to get -6864.

$$-6864+y^{2}=0$$

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.

$$y^{2}-6864=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -6864 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-6864\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-6864\right)}}{2}$$

Multiply -4 times -6864.

$$y=\frac{0±\sqrt{27456}}{2}$$

Take the square root of 27456.

$$y=\frac{0±8\sqrt{429}}{2}$$

Now solve the equation y=\frac{0±8\sqrt{429}}{2} when ± is plus.

$$y=4\sqrt{429}$$

Now solve the equation y=\frac{0±8\sqrt{429}}{2} when ± is minus.

$$y=-4\sqrt{429}$$

The equation is now solved.

$$y=4\sqrt{429} y=-4\sqrt{429}$$