Solve x^2-2(a+7)x+27=0

$$x ^ { 2 } - 2 ( a + 7 ) x + 27 = 0$$

Solve for a

$$a=\frac{x}{2}-7+\frac{27}{2x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 27 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}-2\left(a+7\right)x=-27$$

Use the distributive property to multiply -2 by a+7.

$$x^{2}+\left(-2a-14\right)x=-27$$

Use the distributive property to multiply -2a-14 by x.

$$x^{2}-2ax-14x=-27$$

Subtract x^{2} from both sides.

$$-2ax-14x=-27-x^{2}$$

Add 14x to both sides.

$$-2ax=-27-x^{2}+14x$$

The equation is in standard form.

$$\left(-2x\right)a=-x^{2}+14x-27$$

Divide both sides by -2x.

$$\frac{\left(-2x\right)a}{-2x}=\frac{-x^{2}+14x-27}{-2x}$$

Dividing by -2x undoes the multiplication by -2x.

$$a=\frac{-x^{2}+14x-27}{-2x}$$

Divide -27-x^{2}+14x by -2x.

$$a=\frac{x}{2}-7+\frac{27}{2x}$$

Solve for x (complex solution)

$$x=\sqrt{a^{2}+14a+22}+a+7$$

$$x=-\sqrt{a^{2}+14a+22}+a+7$$

Solve for x

$$x=\sqrt{a^{2}+14a+22}+a+7$$

$$x=-\sqrt{a^{2}+14a+22}+a+7\text{, }a\geq 3\sqrt{3}-7\text{ or }a\leq -3\sqrt{3}-7$$