Solve frac{sqrt{3}}{2}+x^2+x(sqrt{40}

$$\frac { \sqrt { 3 } } { 2 } + x ^ { 2 } + x ( \sqrt { 40 }$$

Evaluate

$$x^{2}+2\sqrt{10}x+\frac{\sqrt{3}}{2}$$

Short Solution Steps

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$\frac{\sqrt{3}}{2}+x^{2}+x\times 2\sqrt{10}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2}+x\times 2\sqrt{10} times \frac{2}{2}.

$$\frac{\sqrt{3}}{2}+\frac{2\left(x^{2}+x\times 2\sqrt{10}\right)}{2}$$

Since \frac{\sqrt{3}}{2} and \frac{2\left(x^{2}+x\times 2\sqrt{10}\right)}{2} have the same denominator, add them by adding their numerators.

$$\frac{\sqrt{3}+2\left(x^{2}+x\times 2\sqrt{10}\right)}{2}$$

Do the multiplications in \sqrt{3}+2\left(x^{2}+x\times 2\sqrt{10}\right).

$$\frac{\sqrt{3}+2x^{2}+4x\sqrt{10}}{2}$$

Factor

$$\frac{2x^{2}+4\sqrt{10}x+\sqrt{3}}{2}$$

Solution Steps

Factor out \frac{1}{2}. Polynomial \sqrt{3}+2x^{2}+4\sqrt{10}x is not factored since it does not have any rational roots.

$$\frac{\sqrt{3}+2x^{2}+4\sqrt{10}x}{2}$$