Solve s^2=41,7+11,1/2*35

$$s ^ { 2 } = \frac { 41,7 + 11,1 } { 2 } \cdot 35$$

Solve for s

$$s=2\sqrt{231}\approx 30.397368307$$

$$s=-2\sqrt{231}\approx -30.397368307$$

Steps by Finding Square Root

Multiply both sides of the equation by 2.

$$2s^{2}=\left(41,7+11,1\right)\times 35$$

Add 41,7 and 11,1 to get 52,8.

$$2s^{2}=52,8\times 35$$

Multiply 52,8 and 35 to get 1848.

$$2s^{2}=1848$$

Divide both sides by 2.

$$s^{2}=\frac{1848}{2}$$

Divide 1848 by 2 to get 924.

$$s^{2}=924$$

Take the square root of both sides of the equation.

$$s=2\sqrt{231} s=-2\sqrt{231}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 2.

$$2s^{2}=\left(41,7+11,1\right)\times 35$$

Add 41,7 and 11,1 to get 52,8.

$$2s^{2}=52,8\times 35$$

Multiply 52,8 and 35 to get 1848.

$$2s^{2}=1848$$

Subtract 1848 from both sides.

$$2s^{2}-1848=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -1848 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$s=\frac{0±\sqrt{0^{2}-4\times 2\left(-1848\right)}}{2\times 2}$$

Square 0.

$$s=\frac{0±\sqrt{-4\times 2\left(-1848\right)}}{2\times 2}$$

Multiply -4 times 2.

$$s=\frac{0±\sqrt{-8\left(-1848\right)}}{2\times 2}$$

Multiply -8 times -1848.

$$s=\frac{0±\sqrt{14784}}{2\times 2}$$

Take the square root of 14784.

$$s=\frac{0±8\sqrt{231}}{2\times 2}$$

Multiply 2 times 2.

$$s=\frac{0±8\sqrt{231}}{4}$$

Now solve the equation s=\frac{0±8\sqrt{231}}{4} when ± is plus.

$$s=2\sqrt{231}$$

Now solve the equation s=\frac{0±8\sqrt{231}}{4} when ± is minus.

$$s=-2\sqrt{231}$$

The equation is now solved.

$$s=2\sqrt{231} s=-2\sqrt{231}$$