Solve frac{88+sqrt{(-88)^2-4(12)(112)}}{2(12)}

$$\frac { 88 + \sqrt { ( - 88 ) ^ { 2 } - 4 ( 12 ) ( 112 ) } } { 2 ( 12 ) }$$

Evaluate

$$\frac{\sqrt{37}+11}{3}\approx 5.694254177$$

Solution Steps

Calculate -88 to the power of 2 and get 7744.

$$\frac{88+\sqrt{7744-4\times 12\times 112}}{2\times 12}$$

Multiply 4 and 12 to get 48.

$$\frac{88+\sqrt{7744-48\times 112}}{2\times 12}$$

Multiply 48 and 112 to get 5376.

$$\frac{88+\sqrt{7744-5376}}{2\times 12}$$

Subtract 5376 from 7744 to get 2368.

$$\frac{88+\sqrt{2368}}{2\times 12}$$

Factor 2368=8^{2}\times 37. Rewrite the square root of the product \sqrt{8^{2}\times 37} as the product of square roots \sqrt{8^{2}}\sqrt{37}. Take the square root of 8^{2}.

$$\frac{88+8\sqrt{37}}{2\times 12}$$

Multiply 2 and 12 to get 24.

$$\frac{88+8\sqrt{37}}{24}$$

Factor

$$\frac{\sqrt{37} + 11}{3} = 5.694254176766073$$