Solve (26x-52)(x-5)/46x-92=0/1

$$\frac { ( 26 x - 52 ) ( x - 5 ) } { 46 x - 92 } = \frac { 0 } { 1 }$$

Solve for x

$$x=5$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by 46\left(x-2\right).

$$\left(26x-52\right)\left(x-5\right)=\left(46x-92\right)\times 0$$

Use the distributive property to multiply 26x-52 by x-5 and combine like terms.

$$26x^{2}-182x+260=\left(46x-92\right)\times 0$$

Anything times zero gives zero.

$$26x^{2}-182x+260=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 26 for a, -182 for b, and 260 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-182\right)±\sqrt{\left(-182\right)^{2}-4\times 26\times 260}}{2\times 26}$$

Square -182.

$$x=\frac{-\left(-182\right)±\sqrt{33124-4\times 26\times 260}}{2\times 26}$$

Multiply -4 times 26.

$$x=\frac{-\left(-182\right)±\sqrt{33124-104\times 260}}{2\times 26}$$

Multiply -104 times 260.

$$x=\frac{-\left(-182\right)±\sqrt{33124-27040}}{2\times 26}$$

Add 33124 to -27040.

$$x=\frac{-\left(-182\right)±\sqrt{6084}}{2\times 26}$$

Take the square root of 6084.

$$x=\frac{-\left(-182\right)±78}{2\times 26}$$

The opposite of -182 is 182.

$$x=\frac{182±78}{2\times 26}$$

Multiply 2 times 26.

$$x=\frac{182±78}{52}$$

Now solve the equation x=\frac{182±78}{52} when ± is plus. Add 182 to 78.

$$x=\frac{260}{52}$$

Divide 260 by 52.

$$x=5$$

Now solve the equation x=\frac{182±78}{52} when ± is minus. Subtract 78 from 182.

$$x=\frac{104}{52}$$

Divide 104 by 52.

$$x=2$$

The equation is now solved.

$$x=5 x=2$$

Variable x cannot be equal to 2.

$$x=5$$

Steps for Completing the Square

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by 46\left(x-2\right).

$$\left(26x-52\right)\left(x-5\right)=\left(46x-92\right)\times 0$$

Use the distributive property to multiply 26x-52 by x-5 and combine like terms.

$$26x^{2}-182x+260=\left(46x-92\right)\times 0$$

Anything times zero gives zero.

$$26x^{2}-182x+260=0$$

Subtract 260 from both sides. Anything subtracted from zero gives its negation.

$$26x^{2}-182x=-260$$

Divide both sides by 26.

$$\frac{26x^{2}-182x}{26}=-\frac{260}{26}$$

Dividing by 26 undoes the multiplication by 26.

$$x^{2}+\left(-\frac{182}{26}\right)x=-\frac{260}{26}$$

Divide -182 by 26.

$$x^{2}-7x=-\frac{260}{26}$$

Divide -260 by 26.

$$x^{2}-7x=-10$$

Divide -7, the coefficient of the x term, by 2 to get -\frac{7}{2}. Then add the square of -\frac{7}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-7x+\left(-\frac{7}{2}\right)^{2}=-10+\left(-\frac{7}{2}\right)^{2}$$

Square -\frac{7}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-7x+\frac{49}{4}=-10+\frac{49}{4}$$

Add -10 to \frac{49}{4}.

$$x^{2}-7x+\frac{49}{4}=\frac{9}{4}$$

Factor x^{2}-7x+\frac{49}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{7}{2}\right)^{2}=\frac{9}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{7}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Simplify.

$$x-\frac{7}{2}=\frac{3}{2} x-\frac{7}{2}=-\frac{3}{2}$$

Add \frac{7}{2} to both sides of the equation.

$$x=5 x=2$$

Variable x cannot be equal to 2.

$$x=5$$