Solve 950/26-4x=x

$$\frac{ 950 }{ 26-4x } = x$$

Solve for x (complex solution)

$$x=\frac{13+\sqrt{3631}i}{4}\approx 3.25+15.064444895i$$

$$x=\frac{-\sqrt{3631}i+13}{4}\approx 3.25-15.064444895i$$

Steps Using the Quadratic Formula

Variable x cannot be equal to \frac{13}{2} since division by zero is not defined. Multiply both sides of the equation by 2\left(-2x+13\right).

$$950=x\times 2\left(-2x+13\right)$$

Use the distributive property to multiply x\times 2 by -2x+13.

$$950=-4x^{2}+13x\times 2$$

Multiply 13 and 2 to get 26.

$$950=-4x^{2}+26x$$

Swap sides so that all variable terms are on the left hand side.

$$-4x^{2}+26x=950$$

Subtract 950 from both sides.

$$-4x^{2}+26x-950=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -4 for a, 26 for b, and -950 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-26±\sqrt{26^{2}-4\left(-4\right)\left(-950\right)}}{2\left(-4\right)}$$

Square 26.

$$x=\frac{-26±\sqrt{676-4\left(-4\right)\left(-950\right)}}{2\left(-4\right)}$$

Multiply -4 times -4.

$$x=\frac{-26±\sqrt{676+16\left(-950\right)}}{2\left(-4\right)}$$

Multiply 16 times -950.

$$x=\frac{-26±\sqrt{676-15200}}{2\left(-4\right)}$$

Add 676 to -15200.

$$x=\frac{-26±\sqrt{-14524}}{2\left(-4\right)}$$

Take the square root of -14524.

$$x=\frac{-26±2\sqrt{3631}i}{2\left(-4\right)}$$

Multiply 2 times -4.

$$x=\frac{-26±2\sqrt{3631}i}{-8}$$

Now solve the equation x=\frac{-26±2\sqrt{3631}i}{-8} when ± is plus. Add -26 to 2i\sqrt{3631}.

$$x=\frac{-26+2\sqrt{3631}i}{-8}$$

Divide -26+2i\sqrt{3631} by -8.

$$x=\frac{-\sqrt{3631}i+13}{4}$$

Now solve the equation x=\frac{-26±2\sqrt{3631}i}{-8} when ± is minus. Subtract 2i\sqrt{3631} from -26.

$$x=\frac{-2\sqrt{3631}i-26}{-8}$$

Divide -26-2i\sqrt{3631} by -8.

$$x=\frac{13+\sqrt{3631}i}{4}$$

The equation is now solved.

$$x=\frac{-\sqrt{3631}i+13}{4} x=\frac{13+\sqrt{3631}i}{4}$$

Steps for Completing the Square

Variable x cannot be equal to \frac{13}{2} since division by zero is not defined. Multiply both sides of the equation by 2\left(-2x+13\right).

$$950=x\times 2\left(-2x+13\right)$$

Use the distributive property to multiply x\times 2 by -2x+13.

$$950=-4x^{2}+13x\times 2$$

Multiply 13 and 2 to get 26.

$$950=-4x^{2}+26x$$

Swap sides so that all variable terms are on the left hand side.

$$-4x^{2}+26x=950$$

Divide both sides by -4.

$$\frac{-4x^{2}+26x}{-4}=\frac{950}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$x^{2}+\frac{26}{-4}x=\frac{950}{-4}$$

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

$$x^{2}-\frac{13}{2}x=\frac{950}{-4}$$

Reduce the fraction \frac{950}{-4} to lowest terms by extracting and canceling out 2.

$$x^{2}-\frac{13}{2}x=-\frac{475}{2}$$

Divide -\frac{13}{2}, the coefficient of the x term, by 2 to get -\frac{13}{4}. Then add the square of -\frac{13}{4} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{13}{2}x+\left(-\frac{13}{4}\right)^{2}=-\frac{475}{2}+\left(-\frac{13}{4}\right)^{2}$$

Square -\frac{13}{4} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{13}{2}x+\frac{169}{16}=-\frac{475}{2}+\frac{169}{16}$$

Add -\frac{475}{2} to \frac{169}{16} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-\frac{13}{2}x+\frac{169}{16}=-\frac{3631}{16}$$

Factor x^{2}-\frac{13}{2}x+\frac{169}{16}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{13}{4}\right)^{2}=-\frac{3631}{16}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{13}{4}\right)^{2}}=\sqrt{-\frac{3631}{16}}$$

Simplify.

$$x-\frac{13}{4}=\frac{\sqrt{3631}i}{4} x-\frac{13}{4}=-\frac{\sqrt{3631}i}{4}$$

Add \frac{13}{4} to both sides of the equation.

$$x=\frac{13+\sqrt{3631}i}{4} x=\frac{-\sqrt{3631}i+13}{4}$$