Solve 965=4w^2+124

$$965 = 4 w ^ { 2 } + 124$$

Solve for w

$$w = \frac{29}{2} = 14\frac{1}{2} = 14.5$$

$$w = -\frac{29}{2} = -14\frac{1}{2} = -14.5$$

Steps Using Difference of Squares

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

$$4w^{2}+124=965$$

Subtract 965 from both sides.

$$4w^{2}+124-965=0$$

Subtract 965 from 124 to get -841.

$$4w^{2}-841=0$$

Consider 4w^{2}-841. Rewrite 4w^{2}-841 as \left(2w\right)^{2}-29^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2w-29\right)\left(2w+29\right)=0$$

To find equation solutions, solve 2w-29=0 and 2w+29=0.

$$w=\frac{29}{2} w=-\frac{29}{2}$$

Steps by Finding Square Root

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

$$4w^{2}+124=965$$

Subtract 124 from both sides.

$$4w^{2}=965-124$$

Subtract 124 from 965 to get 841.

$$4w^{2}=841$$

Divide both sides by 4.

$$w^{2}=\frac{841}{4}$$

Take the square root of both sides of the equation.

$$w=\frac{29}{2} w=-\frac{29}{2}$$

Steps Using the Quadratic Formula

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

$$4w^{2}+124=965$$

Subtract 965 from both sides.

$$4w^{2}+124-965=0$$

Subtract 965 from 124 to get -841.

$$4w^{2}-841=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -841 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{0±\sqrt{0^{2}-4\times 4\left(-841\right)}}{2\times 4}$$

Square 0.

$$w=\frac{0±\sqrt{-4\times 4\left(-841\right)}}{2\times 4}$$

Multiply -4 times 4.

$$w=\frac{0±\sqrt{-16\left(-841\right)}}{2\times 4}$$

Multiply -16 times -841.

$$w=\frac{0±\sqrt{13456}}{2\times 4}$$

Take the square root of 13456.

$$w=\frac{0±116}{2\times 4}$$

Multiply 2 times 4.

$$w=\frac{0±116}{8}$$

Now solve the equation w=\frac{0±116}{8} when ± is plus. Reduce the fraction \frac{116}{8} to lowest terms by extracting and canceling out 4.

$$w=\frac{29}{2}$$

Now solve the equation w=\frac{0±116}{8} when ± is minus. Reduce the fraction \frac{-116}{8} to lowest terms by extracting and canceling out 4.

$$w=-\frac{29}{2}$$

The equation is now solved.

$$w=\frac{29}{2} w=-\frac{29}{2}$$