Solve 4*3^2+10*6^2=c^2

$$4 \cdot 3 ^ { 2 } + 10 \cdot 6 ^ { 2 } = c ^ { 2 }$$

Solve for c

$$c=6\sqrt{11}\approx 19.899748742$$

$$c=-6\sqrt{11}\approx -19.899748742$$

Steps by Finding Square Root

Calculate 3 to the power of 2 and get 9.

$$4\times 9+10\times 6^{2}=c^{2}$$

Multiply 4 and 9 to get 36.

$$36+10\times 6^{2}=c^{2}$$

Calculate 6 to the power of 2 and get 36.

$$36+10\times 36=c^{2}$$

Multiply 10 and 36 to get 360.

$$36+360=c^{2}$$

Add 36 and 360 to get 396.

$$396=c^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$c^{2}=396$$

Take the square root of both sides of the equation.

$$c=6\sqrt{11} c=-6\sqrt{11}$$

Steps Using the Quadratic Formula

Calculate 3 to the power of 2 and get 9.

$$4\times 9+10\times 6^{2}=c^{2}$$

Multiply 4 and 9 to get 36.

$$36+10\times 6^{2}=c^{2}$$

Calculate 6 to the power of 2 and get 36.

$$36+10\times 36=c^{2}$$

Multiply 10 and 36 to get 360.

$$36+360=c^{2}$$

Add 36 and 360 to get 396.

$$396=c^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$c^{2}=396$$

Subtract 396 from both sides.

$$c^{2}-396=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -396 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-396\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-396\right)}}{2}$$

Multiply -4 times -396.

$$c=\frac{0±\sqrt{1584}}{2}$$

Take the square root of 1584.

$$c=\frac{0±12\sqrt{11}}{2}$$

Now solve the equation c=\frac{0±12\sqrt{11}}{2} when ± is plus.

$$c=6\sqrt{11}$$

Now solve the equation c=\frac{0±12\sqrt{11}}{2} when ± is minus.

$$c=-6\sqrt{11}$$

The equation is now solved.

$$c=6\sqrt{11} c=-6\sqrt{11}$$