Solve x^2=3x*7(14x+32)*954

$${ x }^{ 2 } =3x \times 7(14x+32) \times 954$$

Solve for x

$$x = -\frac{641088}{280475} = -2\frac{80138}{280475} \approx -2.285722435$$

$$x=0$$

Steps Using Factoring

Multiply 3 and 7 to get 21.

$$x^{2}=21x\left(14x+32\right)\times 954$$

Multiply 21 and 954 to get 20034.

$$x^{2}=20034x\left(14x+32\right)$$

Use the distributive property to multiply 20034x by 14x+32.

$$x^{2}=280476x^{2}+641088x$$

Subtract 280476x^{2} from both sides.

$$x^{2}-280476x^{2}=641088x$$

Combine x^{2} and -280476x^{2} to get -280475x^{2}.

$$-280475x^{2}=641088x$$

Subtract 641088x from both sides.

$$-280475x^{2}-641088x=0$$

Factor out x.

$$x\left(-280475x-641088\right)=0$$

To find equation solutions, solve x=0 and -280475x-641088=0.

$$x=0 x=-\frac{641088}{280475}$$

Steps Using the Quadratic Formula

Multiply 3 and 7 to get 21.

$$x^{2}=21x\left(14x+32\right)\times 954$$

Multiply 21 and 954 to get 20034.

$$x^{2}=20034x\left(14x+32\right)$$

Use the distributive property to multiply 20034x by 14x+32.

$$x^{2}=280476x^{2}+641088x$$

Subtract 280476x^{2} from both sides.

$$x^{2}-280476x^{2}=641088x$$

Combine x^{2} and -280476x^{2} to get -280475x^{2}.

$$-280475x^{2}=641088x$$

Subtract 641088x from both sides.

$$-280475x^{2}-641088x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -280475 for a, -641088 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-641088\right)±\sqrt{\left(-641088\right)^{2}}}{2\left(-280475\right)}$$

Take the square root of \left(-641088\right)^{2}.

$$x=\frac{-\left(-641088\right)±641088}{2\left(-280475\right)}$$

The opposite of -641088 is 641088.

$$x=\frac{641088±641088}{2\left(-280475\right)}$$

Multiply 2 times -280475.

$$x=\frac{641088±641088}{-560950}$$

Now solve the equation x=\frac{641088±641088}{-560950} when ± is plus. Add 641088 to 641088.

$$x=\frac{1282176}{-560950}$$

Reduce the fraction \frac{1282176}{-560950} to lowest terms by extracting and canceling out 2.

$$x=-\frac{641088}{280475}$$

Now solve the equation x=\frac{641088±641088}{-560950} when ± is minus. Subtract 641088 from 641088.

$$x=\frac{0}{-560950}$$

Divide 0 by -560950.

$$x=0$$

The equation is now solved.

$$x=-\frac{641088}{280475} x=0$$

Steps for Completing the Square

Multiply 3 and 7 to get 21.

$$x^{2}=21x\left(14x+32\right)\times 954$$

Multiply 21 and 954 to get 20034.

$$x^{2}=20034x\left(14x+32\right)$$

Use the distributive property to multiply 20034x by 14x+32.

$$x^{2}=280476x^{2}+641088x$$

Subtract 280476x^{2} from both sides.

$$x^{2}-280476x^{2}=641088x$$

Combine x^{2} and -280476x^{2} to get -280475x^{2}.

$$-280475x^{2}=641088x$$

Subtract 641088x from both sides.

$$-280475x^{2}-641088x=0$$

Divide both sides by -280475.

$$\frac{-280475x^{2}-641088x}{-280475}=\frac{0}{-280475}$$

Dividing by -280475 undoes the multiplication by -280475.

$$x^{2}+\left(-\frac{641088}{-280475}\right)x=\frac{0}{-280475}$$

Divide -641088 by -280475.

$$x^{2}+\frac{641088}{280475}x=\frac{0}{-280475}$$

Divide 0 by -280475.

$$x^{2}+\frac{641088}{280475}x=0$$

Divide \frac{641088}{280475}, the coefficient of the x term, by 2 to get \frac{320544}{280475}. Then add the square of \frac{320544}{280475} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{641088}{280475}x+\left(\frac{320544}{280475}\right)^{2}=\left(\frac{320544}{280475}\right)^{2}$$

Square \frac{320544}{280475} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{641088}{280475}x+\frac{102748455936}{78666225625}=\frac{102748455936}{78666225625}$$

Factor x^{2}+\frac{641088}{280475}x+\frac{102748455936}{78666225625}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{320544}{280475}\right)^{2}=\frac{102748455936}{78666225625}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{320544}{280475}\right)^{2}}=\sqrt{\frac{102748455936}{78666225625}}$$

Simplify.

$$x+\frac{320544}{280475}=\frac{320544}{280475} x+\frac{320544}{280475}=-\frac{320544}{280475}$$

Subtract \frac{320544}{280475} from both sides of the equation.

$$x=0 x=-\frac{641088}{280475}$$