(x-9)(x-9)=294

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Solution for (x-9)(x-9)=294 equation:


Simplifying
(x + -9)(x + -9) = 294

Reorder the terms:
(-9 + x)(x + -9) = 294

Reorder the terms:
(-9 + x)(-9 + x) = 294

Multiply (-9 + x) * (-9 + x)
(-9(-9 + x) + x(-9 + x)) = 294
((-9 * -9 + x * -9) + x(-9 + x)) = 294
((81 + -9x) + x(-9 + x)) = 294
(81 + -9x + (-9 * x + x * x)) = 294
(81 + -9x + (-9x + x2)) = 294

Combine like terms: -9x + -9x = -18x
(81 + -18x + x2) = 294

Solving
81 + -18x + x2 = 294

Solving for variable 'x'.

Reorder the terms:
81 + -294 + -18x + x2 = 294 + -294

Combine like terms: 81 + -294 = -213
-213 + -18x + x2 = 294 + -294

Combine like terms: 294 + -294 = 0
-213 + -18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '213' to each side of the equation.
-213 + -18x + 213 + x2 = 0 + 213

Reorder the terms:
-213 + 213 + -18x + x2 = 0 + 213

Combine like terms: -213 + 213 = 0
0 + -18x + x2 = 0 + 213
-18x + x2 = 0 + 213

Combine like terms: 0 + 213 = 213
-18x + x2 = 213

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = 213 + 81

Reorder the terms:
81 + -18x + x2 = 213 + 81

Combine like terms: 213 + 81 = 294
81 + -18x + x2 = 294

Factor a perfect square on the left side:
(x + -9)(x + -9) = 294

Calculate the square root of the right side: 17.146428199

Break this problem into two subproblems by setting 
(x + -9) equal to 17.146428199 and -17.146428199.

Subproblem 1

x + -9 = 17.146428199 Simplifying x + -9 = 17.146428199 Reorder the terms: -9 + x = 17.146428199 Solving -9 + x = 17.146428199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 17.146428199 + 9 Combine like terms: -9 + 9 = 0 0 + x = 17.146428199 + 9 x = 17.146428199 + 9 Combine like terms: 17.146428199 + 9 = 26.146428199 x = 26.146428199 Simplifying x = 26.146428199

Subproblem 2

x + -9 = -17.146428199 Simplifying x + -9 = -17.146428199 Reorder the terms: -9 + x = -17.146428199 Solving -9 + x = -17.146428199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -17.146428199 + 9 Combine like terms: -9 + 9 = 0 0 + x = -17.146428199 + 9 x = -17.146428199 + 9 Combine like terms: -17.146428199 + 9 = -8.146428199 x = -8.146428199 Simplifying x = -8.146428199

Solution

The solution to the problem is based on the solutions from the subproblems. x = {26.146428199, -8.146428199}

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