Solve 471+157=628(m^2)

$$471 + 157 = 628 ( m ^ { 2 } )$$

Solve for m

$$m=1$$

$$m=-1$$

Steps Using Difference of Squares

Add 471 and 157 to get 628.

$$628=628m^{2}$$

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

$$628m^{2}=628$$

Subtract 628 from both sides.

$$628m^{2}-628=0$$

Divide both sides by 628.

$$m^{2}-1=0$$

Consider m^{2}-1. Rewrite m^{2}-1 as m^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(m-1\right)\left(m+1\right)=0$$

To find equation solutions, solve m-1=0 and m+1=0.

$$m=1 m=-1$$

Steps by Finding Square Root

Add 471 and 157 to get 628.

$$628=628m^{2}$$

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

$$628m^{2}=628$$

Divide both sides by 628.

$$m^{2}=\frac{628}{628}$$

Divide 628 by 628 to get 1.

$$m^{2}=1$$

Take the square root of both sides of the equation.

$$m=1 m=-1$$

Steps Using the Quadratic Formula

Add 471 and 157 to get 628.

$$628=628m^{2}$$

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

$$628m^{2}=628$$

Subtract 628 from both sides.

$$628m^{2}-628=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 628 for a, 0 for b, and -628 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\times 628\left(-628\right)}}{2\times 628}$$

Square 0.

$$m=\frac{0±\sqrt{-4\times 628\left(-628\right)}}{2\times 628}$$

Multiply -4 times 628.

$$m=\frac{0±\sqrt{-2512\left(-628\right)}}{2\times 628}$$

Multiply -2512 times -628.

$$m=\frac{0±\sqrt{1577536}}{2\times 628}$$

Take the square root of 1577536.

$$m=\frac{0±1256}{2\times 628}$$

Multiply 2 times 628.

$$m=\frac{0±1256}{1256}$$

Now solve the equation m=\frac{0±1256}{1256} when ± is plus. Divide 1256 by 1256.

$$m=1$$

Now solve the equation m=\frac{0±1256}{1256} when ± is minus. Divide -1256 by 1256.

$$m=-1$$

The equation is now solved.

$$m=1 m=-1$$