Solve (7x-5)(2x+1)=5*(5*7x^2-2x)*2

$$( 7 x - 5 ) ( 2 x + 1 ) = 5 \cdot ( 5 \cdot 7 x ^ { 2 } - 2 x ) \times 2$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{6431}i+17}{672}\approx 0.025297619-0.119335589i$$

$$x=\frac{17+\sqrt{6431}i}{672}\approx 0.025297619+0.119335589i$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 7x-5 by 2x+1 and combine like terms.

$$14x^{2}-3x-5=5\left(5\times 7x^{2}-2x\right)\times 2$$

Multiply 5 and 7 to get 35.

$$14x^{2}-3x-5=5\left(35x^{2}-2x\right)\times 2$$

Multiply 5 and 2 to get 10.

$$14x^{2}-3x-5=10\left(35x^{2}-2x\right)$$

Use the distributive property to multiply 10 by 35x^{2}-2x.

$$14x^{2}-3x-5=350x^{2}-20x$$

Subtract 350x^{2} from both sides.

$$14x^{2}-3x-5-350x^{2}=-20x$$

Combine 14x^{2} and -350x^{2} to get -336x^{2}.

$$-336x^{2}-3x-5=-20x$$

Add 20x to both sides.

$$-336x^{2}-3x-5+20x=0$$

Combine -3x and 20x to get 17x.

$$-336x^{2}+17x-5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -336 for a, 17 for b, and -5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-17±\sqrt{17^{2}-4\left(-336\right)\left(-5\right)}}{2\left(-336\right)}$$

Square 17.

$$x=\frac{-17±\sqrt{289-4\left(-336\right)\left(-5\right)}}{2\left(-336\right)}$$

Multiply -4 times -336.

$$x=\frac{-17±\sqrt{289+1344\left(-5\right)}}{2\left(-336\right)}$$

Multiply 1344 times -5.

$$x=\frac{-17±\sqrt{289-6720}}{2\left(-336\right)}$$

Add 289 to -6720.

$$x=\frac{-17±\sqrt{-6431}}{2\left(-336\right)}$$

Take the square root of -6431.

$$x=\frac{-17±\sqrt{6431}i}{2\left(-336\right)}$$

Multiply 2 times -336.

$$x=\frac{-17±\sqrt{6431}i}{-672}$$

Now solve the equation x=\frac{-17±\sqrt{6431}i}{-672} when ± is plus. Add -17 to i\sqrt{6431}.

$$x=\frac{-17+\sqrt{6431}i}{-672}$$

Divide -17+i\sqrt{6431} by -672.

$$x=\frac{-\sqrt{6431}i+17}{672}$$

Now solve the equation x=\frac{-17±\sqrt{6431}i}{-672} when ± is minus. Subtract i\sqrt{6431} from -17.

$$x=\frac{-\sqrt{6431}i-17}{-672}$$

Divide -17-i\sqrt{6431} by -672.

$$x=\frac{17+\sqrt{6431}i}{672}$$

The equation is now solved.

$$x=\frac{-\sqrt{6431}i+17}{672} x=\frac{17+\sqrt{6431}i}{672}$$

Steps for Completing the Square

Use the distributive property to multiply 7x-5 by 2x+1 and combine like terms.

$$14x^{2}-3x-5=5\left(5\times 7x^{2}-2x\right)\times 2$$

Multiply 5 and 7 to get 35.

$$14x^{2}-3x-5=5\left(35x^{2}-2x\right)\times 2$$

Multiply 5 and 2 to get 10.

$$14x^{2}-3x-5=10\left(35x^{2}-2x\right)$$

Use the distributive property to multiply 10 by 35x^{2}-2x.

$$14x^{2}-3x-5=350x^{2}-20x$$

Subtract 350x^{2} from both sides.

$$14x^{2}-3x-5-350x^{2}=-20x$$

Combine 14x^{2} and -350x^{2} to get -336x^{2}.

$$-336x^{2}-3x-5=-20x$$

Add 20x to both sides.

$$-336x^{2}-3x-5+20x=0$$

Combine -3x and 20x to get 17x.

$$-336x^{2}+17x-5=0$$

Add 5 to both sides. Anything plus zero gives itself.

$$-336x^{2}+17x=5$$

Divide both sides by -336.

$$\frac{-336x^{2}+17x}{-336}=\frac{5}{-336}$$

Dividing by -336 undoes the multiplication by -336.

$$x^{2}+\frac{17}{-336}x=\frac{5}{-336}$$

Divide 17 by -336.

$$x^{2}-\frac{17}{336}x=\frac{5}{-336}$$

Divide 5 by -336.

$$x^{2}-\frac{17}{336}x=-\frac{5}{336}$$

Divide -\frac{17}{336}, the coefficient of the x term, by 2 to get -\frac{17}{672}. Then add the square of -\frac{17}{672} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{17}{336}x+\left(-\frac{17}{672}\right)^{2}=-\frac{5}{336}+\left(-\frac{17}{672}\right)^{2}$$

Square -\frac{17}{672} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{17}{336}x+\frac{289}{451584}=-\frac{5}{336}+\frac{289}{451584}$$

Add -\frac{5}{336} to \frac{289}{451584} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-\frac{17}{336}x+\frac{289}{451584}=-\frac{6431}{451584}$$

Factor x^{2}-\frac{17}{336}x+\frac{289}{451584}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{17}{672}\right)^{2}=-\frac{6431}{451584}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{17}{672}\right)^{2}}=\sqrt{-\frac{6431}{451584}}$$

Simplify.

$$x-\frac{17}{672}=\frac{\sqrt{6431}i}{672} x-\frac{17}{672}=-\frac{\sqrt{6431}i}{672}$$

Add \frac{17}{672} to both sides of the equation.

$$x=\frac{17+\sqrt{6431}i}{672} x=\frac{-\sqrt{6431}i+17}{672}$$