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Simplifying 3x2 + 6x + -456 = 0 Reorder the terms: -456 + 6x + 3x2 = 0 Solving -456 + 6x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-152 + 2x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-152 + 2x + x2)' equal to zero and attempt to solve: Simplifying -152 + 2x + x2 = 0 Solving -152 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '152' to each side of the equation. -152 + 2x + 152 + x2 = 0 + 152 Reorder the terms: -152 + 152 + 2x + x2 = 0 + 152 Combine like terms: -152 + 152 = 0 0 + 2x + x2 = 0 + 152 2x + x2 = 0 + 152 Combine like terms: 0 + 152 = 152 2x + x2 = 152 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 = 152 + 1 Reorder the terms: 1 + 2x + x2 = 152 + 1 Combine like terms: 152 + 1 = 153 1 + 2x + x2 = 153 Factor a perfect square on the left side: (x + 1)(x + 1) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (x + 1) equal to 12.369316877 and -12.369316877.Subproblem 1
x + 1 = 12.369316877 Simplifying x + 1 = 12.369316877 Reorder the terms: 1 + x = 12.369316877 Solving 1 + x = 12.369316877 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 = 12.369316877 + -1 Combine like terms: 1 + -1 = 0 0 + x = 12.369316877 + -1 x = 12.369316877 + -1 Combine like terms: 12.369316877 + -1 = 11.369316877 x = 11.369316877 Simplifying x = 11.369316877Subproblem 2
x + 1 = -12.369316877 Simplifying x + 1 = -12.369316877 Reorder the terms: 1 + x = -12.369316877 Solving 1 + x = -12.369316877 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 = -12.369316877 + -1 Combine like terms: 1 + -1 = 0 0 + x = -12.369316877 + -1 x = -12.369316877 + -1 Combine like terms: -12.369316877 + -1 = -13.369316877 x = -13.369316877 Simplifying x = -13.369316877Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.369316877, -13.369316877}Solution
x = {11.369316877, -13.369316877}
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