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Simplifying x2 + -144x + 984 = 0 Reorder the terms: 984 + -144x + x2 = 0 Solving 984 + -144x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-984' to each side of the equation. 984 + -144x + -984 + x2 = 0 + -984 Reorder the terms: 984 + -984 + -144x + x2 = 0 + -984 Combine like terms: 984 + -984 = 0 0 + -144x + x2 = 0 + -984 -144x + x2 = 0 + -984 Combine like terms: 0 + -984 = -984 -144x + x2 = -984 The x term is -144x. Take half its coefficient (-72). Square it (5184) and add it to both sides. Add '5184' to each side of the equation. -144x + 5184 + x2 = -984 + 5184 Reorder the terms: 5184 + -144x + x2 = -984 + 5184 Combine like terms: -984 + 5184 = 4200 5184 + -144x + x2 = 4200 Factor a perfect square on the left side: (x + -72)(x + -72) = 4200 Calculate the square root of the right side: 64.807406984 Break this problem into two subproblems by setting (x + -72) equal to 64.807406984 and -64.807406984.Subproblem 1
x + -72 = 64.807406984 Simplifying x + -72 = 64.807406984 Reorder the terms: -72 + x = 64.807406984 Solving -72 + x = 64.807406984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '72' to each side of the equation. -72 + 72 + x = 64.807406984 + 72 Combine like terms: -72 + 72 = 0 0 + x = 64.807406984 + 72 x = 64.807406984 + 72 Combine like terms: 64.807406984 + 72 = 136.807406984 x = 136.807406984 Simplifying x = 136.807406984Subproblem 2
x + -72 = -64.807406984 Simplifying x + -72 = -64.807406984 Reorder the terms: -72 + x = -64.807406984 Solving -72 + x = -64.807406984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '72' to each side of the equation. -72 + 72 + x = -64.807406984 + 72 Combine like terms: -72 + 72 = 0 0 + x = -64.807406984 + 72 x = -64.807406984 + 72 Combine like terms: -64.807406984 + 72 = 7.192593016 x = 7.192593016 Simplifying x = 7.192593016Solution
The solution to the problem is based on the solutions from the subproblems. x = {136.807406984, 7.192593016}
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