Solve 26x^2+25x*59=0

$$26 { x }^{ 2 } +25x \times 59=0$$

Solve for x

$$x = -\frac{1475}{26} = -56\frac{19}{26} \approx -56.730769231$$

$$x=0$$

Steps Using Factoring

Factor out x.

$$x\left(26x+25\times 59\right)=0$$

To find equation solutions, solve x=0 and 26x+1475=0.

$$x=0 x=-\frac{1475}{26}$$

Steps Using the Quadratic Formula

Multiply 25 and 59 to get 1475.

$$26x^{2}+1475x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 26 for a, 1475 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1475±\sqrt{1475^{2}}}{2\times 26}$$

Take the square root of 1475^{2}.

$$x=\frac{-1475±1475}{2\times 26}$$

Multiply 2 times 26.

$$x=\frac{-1475±1475}{52}$$

Now solve the equation x=\frac{-1475±1475}{52} when ± is plus. Add -1475 to 1475.

$$x=\frac{0}{52}$$

Divide 0 by 52.

$$x=0$$

Now solve the equation x=\frac{-1475±1475}{52} when ± is minus. Subtract 1475 from -1475.

$$x=-\frac{2950}{52}$$

Reduce the fraction \frac{-2950}{52} to lowest terms by extracting and canceling out 2.

$$x=-\frac{1475}{26}$$

The equation is now solved.

$$x=0 x=-\frac{1475}{26}$$

Steps for Completing the Square

Multiply 25 and 59 to get 1475.

$$26x^{2}+1475x=0$$

Divide both sides by 26.

$$\frac{26x^{2}+1475x}{26}=\frac{0}{26}$$

Dividing by 26 undoes the multiplication by 26.

$$x^{2}+\frac{1475}{26}x=\frac{0}{26}$$

Divide 0 by 26.

$$x^{2}+\frac{1475}{26}x=0$$

Divide \frac{1475}{26}, the coefficient of the x term, by 2 to get \frac{1475}{52}. Then add the square of \frac{1475}{52} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{1475}{26}x+\left(\frac{1475}{52}\right)^{2}=\left(\frac{1475}{52}\right)^{2}$$

Square \frac{1475}{52} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{1475}{26}x+\frac{2175625}{2704}=\frac{2175625}{2704}$$

Factor x^{2}+\frac{1475}{26}x+\frac{2175625}{2704}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{1475}{52}\right)^{2}=\frac{2175625}{2704}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{1475}{52}\right)^{2}}=\sqrt{\frac{2175625}{2704}}$$

Simplify.

$$x+\frac{1475}{52}=\frac{1475}{52} x+\frac{1475}{52}=-\frac{1475}{52}$$

Subtract \frac{1475}{52} from both sides of the equation.

$$x=0 x=-\frac{1475}{26}$$