Solve 05x+4x^2=26

$$05x+4 { x }^{ 2 } =26$$

Solve for x

$$x = \frac{\sqrt{26}}{2} \approx 2.549509757$$

$$x = -\frac{\sqrt{26}}{2} \approx -2.549509757$$

Steps by Finding Square Root

Multiply 0 and 5 to get 0.

$$0x+4x^{2}=26$$

Anything times zero gives zero.

$$0+4x^{2}=26$$

Anything plus zero gives itself.

$$4x^{2}=26$$

Divide both sides by 4.

$$x^{2}=\frac{26}{4}$$

Reduce the fraction \frac{26}{4} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{13}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{26}}{2} x=-\frac{\sqrt{26}}{2}$$

Steps Using the Quadratic Formula

Multiply 0 and 5 to get 0.

$$0x+4x^{2}=26$$

Anything times zero gives zero.

$$0+4x^{2}=26$$

Anything plus zero gives itself.

$$4x^{2}=26$$

Subtract 26 from both sides.

$$4x^{2}-26=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -26 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-26\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-26\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-26\right)}}{2\times 4}$$

Multiply -16 times -26.

$$x=\frac{0±\sqrt{416}}{2\times 4}$$

Take the square root of 416.

$$x=\frac{0±4\sqrt{26}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±4\sqrt{26}}{8}$$

Now solve the equation x=\frac{0±4\sqrt{26}}{8} when ± is plus.

$$x=\frac{\sqrt{26}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{26}}{8} when ± is minus.

$$x=-\frac{\sqrt{26}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{26}}{2} x=-\frac{\sqrt{26}}{2}$$