Solve 10^2+b^2=26^2

$$10 ^ { 2 } + b ^ { 2 } = 26 ^ { 2 }$$

Solve for b

$$b=-24$$

$$b=24$$

Steps Using Difference of Squares

Calculate 10 to the power of 2 and get 100.

$$100+b^{2}=26^{2}$$

Calculate 26 to the power of 2 and get 676.

$$100+b^{2}=676$$

Subtract 676 from both sides.

$$100+b^{2}-676=0$$

Subtract 676 from 100 to get -576.

$$-576+b^{2}=0$$

Consider -576+b^{2}. Rewrite -576+b^{2} as b^{2}-24^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(b-24\right)\left(b+24\right)=0$$

To find equation solutions, solve b-24=0 and b+24=0.

$$b=24 b=-24$$

Steps by Finding Square Root

Calculate 10 to the power of 2 and get 100.

$$100+b^{2}=26^{2}$$

Calculate 26 to the power of 2 and get 676.

$$100+b^{2}=676$$

Subtract 100 from both sides.

$$b^{2}=676-100$$

Subtract 100 from 676 to get 576.

$$b^{2}=576$$

Take the square root of both sides of the equation.

$$b=24 b=-24$$

Steps Using the Quadratic Formula

Calculate 10 to the power of 2 and get 100.

$$100+b^{2}=26^{2}$$

Calculate 26 to the power of 2 and get 676.

$$100+b^{2}=676$$

Subtract 676 from both sides.

$$100+b^{2}-676=0$$

Subtract 676 from 100 to get -576.

$$-576+b^{2}=0$$

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.

$$b^{2}-576=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -576 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-576\right)}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-576\right)}}{2}$$

Multiply -4 times -576.

$$b=\frac{0±\sqrt{2304}}{2}$$

Take the square root of 2304.

$$b=\frac{0±48}{2}$$

Now solve the equation b=\frac{0±48}{2} when ± is plus. Divide 48 by 2.

$$b=24$$

Now solve the equation b=\frac{0±48}{2} when ± is minus. Divide -48 by 2.

$$b=-24$$

The equation is now solved.

$$b=24 b=-24$$