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Simplifying 3x2 + -6x + -528 = 0 Reorder the terms: -528 + -6x + 3x2 = 0 Solving -528 + -6x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-176 + -2x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-176 + -2x + x2)' equal to zero and attempt to solve: Simplifying -176 + -2x + x2 = 0 Solving -176 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '176' to each side of the equation. -176 + -2x + 176 + x2 = 0 + 176 Reorder the terms: -176 + 176 + -2x + x2 = 0 + 176 Combine like terms: -176 + 176 = 0 0 + -2x + x2 = 0 + 176 -2x + x2 = 0 + 176 Combine like terms: 0 + 176 = 176 -2x + x2 = 176 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 176 + 1 Reorder the terms: 1 + -2x + x2 = 176 + 1 Combine like terms: 176 + 1 = 177 1 + -2x + x2 = 177 Factor a perfect square on the left side: (x + -1)(x + -1) = 177 Calculate the square root of the right side: 13.304134696 Break this problem into two subproblems by setting (x + -1) equal to 13.304134696 and -13.304134696.Subproblem 1
x + -1 = 13.304134696 Simplifying x + -1 = 13.304134696 Reorder the terms: -1 + x = 13.304134696 Solving -1 + x = 13.304134696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 13.304134696 + 1 Combine like terms: -1 + 1 = 0 0 + x = 13.304134696 + 1 x = 13.304134696 + 1 Combine like terms: 13.304134696 + 1 = 14.304134696 x = 14.304134696 Simplifying x = 14.304134696Subproblem 2
x + -1 = -13.304134696 Simplifying x + -1 = -13.304134696 Reorder the terms: -1 + x = -13.304134696 Solving -1 + x = -13.304134696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -13.304134696 + 1 Combine like terms: -1 + 1 = 0 0 + x = -13.304134696 + 1 x = -13.304134696 + 1 Combine like terms: -13.304134696 + 1 = -12.304134696 x = -12.304134696 Simplifying x = -12.304134696Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.304134696, -12.304134696}Solution
x = {14.304134696, -12.304134696}
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