Solve 47-x(3x+4)=2(17-2x)-62

$$47 - x ( 3 x + 4 ) = 2 ( 17 - 2 x ) - 62$$

Solve for x

$$x=5$$

$$x=-5$$

Steps by Finding Square Root

Use the distributive property to multiply x by 3x+4.

$$47-\left(3x^{2}+4x\right)=2\left(17-2x\right)-62$$

To find the opposite of 3x^{2}+4x, find the opposite of each term.

$$47-3x^{2}-4x=2\left(17-2x\right)-62$$

Use the distributive property to multiply 2 by 17-2x.

$$47-3x^{2}-4x=34-4x-62$$

Subtract 62 from 34 to get -28.

$$47-3x^{2}-4x=-28-4x$$

Add 4x to both sides.

$$47-3x^{2}-4x+4x=-28$$

Combine -4x and 4x to get 0.

$$47-3x^{2}=-28$$

Subtract 47 from both sides.

$$-3x^{2}=-28-47$$

Subtract 47 from -28 to get -75.

$$-3x^{2}=-75$$

Divide both sides by -3.

$$x^{2}=\frac{-75}{-3}$$

Divide -75 by -3 to get 25.

$$x^{2}=25$$

Take the square root of both sides of the equation.

$$x=5 x=-5$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x by 3x+4.

$$47-\left(3x^{2}+4x\right)=2\left(17-2x\right)-62$$

To find the opposite of 3x^{2}+4x, find the opposite of each term.

$$47-3x^{2}-4x=2\left(17-2x\right)-62$$

Use the distributive property to multiply 2 by 17-2x.

$$47-3x^{2}-4x=34-4x-62$$

Subtract 62 from 34 to get -28.

$$47-3x^{2}-4x=-28-4x$$

Subtract -28 from both sides.

$$47-3x^{2}-4x-\left(-28\right)=-4x$$

The opposite of -28 is 28.

$$47-3x^{2}-4x+28=-4x$$

Add 4x to both sides.

$$47-3x^{2}-4x+28+4x=0$$

Add 47 and 28 to get 75.

$$75-3x^{2}-4x+4x=0$$

Combine -4x and 4x to get 0.

$$75-3x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-3x^{2}+75=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 0 for b, and 75 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)\times 75}}{2\left(-3\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3\right)\times 75}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{0±\sqrt{12\times 75}}{2\left(-3\right)}$$

Multiply 12 times 75.

$$x=\frac{0±\sqrt{900}}{2\left(-3\right)}$$

Take the square root of 900.

$$x=\frac{0±30}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{0±30}{-6}$$

Now solve the equation x=\frac{0±30}{-6} when ± is plus. Divide 30 by -6.

$$x=-5$$

Now solve the equation x=\frac{0±30}{-6} when ± is minus. Divide -30 by -6.

$$x=5$$

The equation is now solved.

$$x=-5 x=5$$