Solve 10*10=b^2*2

$$10 \times 10 = b ^ { 2 } \times 2$$

Solve for b

$$b=5\sqrt{2}\approx 7.071067812$$

$$b=-5\sqrt{2}\approx -7.071067812$$

Steps by Finding Square Root

Multiply 10 and 10 to get 100.

$$100=b^{2}\times 2$$

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

$$b^{2}\times 2=100$$

Divide both sides by 2.

$$b^{2}=\frac{100}{2}$$

Divide 100 by 2 to get 50.

$$b^{2}=50$$

Take the square root of both sides of the equation.

$$b=5\sqrt{2} b=-5\sqrt{2}$$

Steps Using the Quadratic Formula

Multiply 10 and 10 to get 100.

$$100=b^{2}\times 2$$

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

$$b^{2}\times 2=100$$

Subtract 100 from both sides.

$$b^{2}\times 2-100=0$$

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.

$$2b^{2}-100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\times 2\left(-100\right)}}{2\times 2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\times 2\left(-100\right)}}{2\times 2}$$

Multiply -4 times 2.

$$b=\frac{0±\sqrt{-8\left(-100\right)}}{2\times 2}$$

Multiply -8 times -100.

$$b=\frac{0±\sqrt{800}}{2\times 2}$$

Take the square root of 800.

$$b=\frac{0±20\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$b=\frac{0±20\sqrt{2}}{4}$$

Now solve the equation b=\frac{0±20\sqrt{2}}{4} when ± is plus.

$$b=5\sqrt{2}$$

Now solve the equation b=\frac{0±20\sqrt{2}}{4} when ± is minus.

$$b=-5\sqrt{2}$$

The equation is now solved.

$$b=5\sqrt{2} b=-5\sqrt{2}$$