Solve 7x*8x+14x=3266

$$7x \times 8x+14x=3266$$

Solve for x

$$x=\frac{\sqrt{182945}}{56}-\frac{1}{8}\approx 7.512869701$$

$$x=-\frac{\sqrt{182945}}{56}-\frac{1}{8}\approx -7.762869701$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$7x^{2}\times 8+14x=3266$$

Multiply 7 and 8 to get 56.

$$56x^{2}+14x=3266$$

Subtract 3266 from both sides.

$$56x^{2}+14x-3266=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 56 for a, 14 for b, and -3266 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-14±\sqrt{14^{2}-4\times 56\left(-3266\right)}}{2\times 56}$$

Square 14.

$$x=\frac{-14±\sqrt{196-4\times 56\left(-3266\right)}}{2\times 56}$$

Multiply -4 times 56.

$$x=\frac{-14±\sqrt{196-224\left(-3266\right)}}{2\times 56}$$

Multiply -224 times -3266.

$$x=\frac{-14±\sqrt{196+731584}}{2\times 56}$$

Add 196 to 731584.

$$x=\frac{-14±\sqrt{731780}}{2\times 56}$$

Take the square root of 731780.

$$x=\frac{-14±2\sqrt{182945}}{2\times 56}$$

Multiply 2 times 56.

$$x=\frac{-14±2\sqrt{182945}}{112}$$

Now solve the equation x=\frac{-14±2\sqrt{182945}}{112} when ± is plus. Add -14 to 2\sqrt{182945}.

$$x=\frac{2\sqrt{182945}-14}{112}$$

Divide -14+2\sqrt{182945} by 112.

$$x=\frac{\sqrt{182945}}{56}-\frac{1}{8}$$

Now solve the equation x=\frac{-14±2\sqrt{182945}}{112} when ± is minus. Subtract 2\sqrt{182945} from -14.

$$x=\frac{-2\sqrt{182945}-14}{112}$$

Divide -14-2\sqrt{182945} by 112.

$$x=-\frac{\sqrt{182945}}{56}-\frac{1}{8}$$

The equation is now solved.

$$x=\frac{\sqrt{182945}}{56}-\frac{1}{8} x=-\frac{\sqrt{182945}}{56}-\frac{1}{8}$$

Steps for Completing the Square

Multiply x and x to get x^{2}.

$$7x^{2}\times 8+14x=3266$$

Multiply 7 and 8 to get 56.

$$56x^{2}+14x=3266$$

Divide both sides by 56.

$$\frac{56x^{2}+14x}{56}=\frac{3266}{56}$$

Dividing by 56 undoes the multiplication by 56.

$$x^{2}+\frac{14}{56}x=\frac{3266}{56}$$

Reduce the fraction \frac{14}{56} to lowest terms by extracting and canceling out 14.

$$x^{2}+\frac{1}{4}x=\frac{3266}{56}$$

Reduce the fraction \frac{3266}{56} to lowest terms by extracting and canceling out 2.

$$x^{2}+\frac{1}{4}x=\frac{1633}{28}$$

Divide \frac{1}{4}, the coefficient of the x term, by 2 to get \frac{1}{8}. Then add the square of \frac{1}{8} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{1}{4}x+\left(\frac{1}{8}\right)^{2}=\frac{1633}{28}+\left(\frac{1}{8}\right)^{2}$$

Square \frac{1}{8} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{1}{4}x+\frac{1}{64}=\frac{1633}{28}+\frac{1}{64}$$

Add \frac{1633}{28} to \frac{1}{64} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{1}{4}x+\frac{1}{64}=\frac{26135}{448}$$

Factor x^{2}+\frac{1}{4}x+\frac{1}{64}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{1}{8}\right)^{2}=\frac{26135}{448}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{1}{8}\right)^{2}}=\sqrt{\frac{26135}{448}}$$

Simplify.

$$x+\frac{1}{8}=\frac{\sqrt{182945}}{56} x+\frac{1}{8}=-\frac{\sqrt{182945}}{56}$$

Subtract \frac{1}{8} from both sides of the equation.

$$x=\frac{\sqrt{182945}}{56}-\frac{1}{8} x=-\frac{\sqrt{182945}}{56}-\frac{1}{8}$$