x(x-9)=167

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Solution for x(x-9)=167 equation:


Simplifying
x(x + -9) = 167

Reorder the terms:
x(-9 + x) = 167
(-9 * x + x * x) = 167
(-9x + x2) = 167

Solving
-9x + x2 = 167

Solving for variable 'x'.

Reorder the terms:
-167 + -9x + x2 = 167 + -167

Combine like terms: 167 + -167 = 0
-167 + -9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '167' to each side of the equation.
-167 + -9x + 167 + x2 = 0 + 167

Reorder the terms:
-167 + 167 + -9x + x2 = 0 + 167

Combine like terms: -167 + 167 = 0
0 + -9x + x2 = 0 + 167
-9x + x2 = 0 + 167

Combine like terms: 0 + 167 = 167
-9x + x2 = 167

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 167 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 167 + 20.25

Combine like terms: 167 + 20.25 = 187.25
20.25 + -9x + x2 = 187.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 187.25

Calculate the square root of the right side: 13.683932183

Break this problem into two subproblems by setting 
(x + -4.5) equal to 13.683932183 and -13.683932183.

Subproblem 1

x + -4.5 = 13.683932183 Simplifying x + -4.5 = 13.683932183 Reorder the terms: -4.5 + x = 13.683932183 Solving -4.5 + x = 13.683932183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 13.683932183 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 13.683932183 + 4.5 x = 13.683932183 + 4.5 Combine like terms: 13.683932183 + 4.5 = 18.183932183 x = 18.183932183 Simplifying x = 18.183932183

Subproblem 2

x + -4.5 = -13.683932183 Simplifying x + -4.5 = -13.683932183 Reorder the terms: -4.5 + x = -13.683932183 Solving -4.5 + x = -13.683932183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -13.683932183 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -13.683932183 + 4.5 x = -13.683932183 + 4.5 Combine like terms: -13.683932183 + 4.5 = -9.183932183 x = -9.183932183 Simplifying x = -9.183932183

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.183932183, -9.183932183}

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