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Simplifying 2x2 + -6x + -312 = 0 Reorder the terms: -312 + -6x + 2x2 = 0 Solving -312 + -6x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-156 + -3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-156 + -3x + x2)' equal to zero and attempt to solve: Simplifying -156 + -3x + x2 = 0 Solving -156 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '156' to each side of the equation. -156 + -3x + 156 + x2 = 0 + 156 Reorder the terms: -156 + 156 + -3x + x2 = 0 + 156 Combine like terms: -156 + 156 = 0 0 + -3x + x2 = 0 + 156 -3x + x2 = 0 + 156 Combine like terms: 0 + 156 = 156 -3x + x2 = 156 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 156 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 156 + 2.25 Combine like terms: 156 + 2.25 = 158.25 2.25 + -3x + x2 = 158.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 158.25 Calculate the square root of the right side: 12.579745625 Break this problem into two subproblems by setting (x + -1.5) equal to 12.579745625 and -12.579745625.Subproblem 1
x + -1.5 = 12.579745625 Simplifying x + -1.5 = 12.579745625 Reorder the terms: -1.5 + x = 12.579745625 Solving -1.5 + x = 12.579745625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 12.579745625 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 12.579745625 + 1.5 x = 12.579745625 + 1.5 Combine like terms: 12.579745625 + 1.5 = 14.079745625 x = 14.079745625 Simplifying x = 14.079745625Subproblem 2
x + -1.5 = -12.579745625 Simplifying x + -1.5 = -12.579745625 Reorder the terms: -1.5 + x = -12.579745625 Solving -1.5 + x = -12.579745625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -12.579745625 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -12.579745625 + 1.5 x = -12.579745625 + 1.5 Combine like terms: -12.579745625 + 1.5 = -11.079745625 x = -11.079745625 Simplifying x = -11.079745625Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.079745625, -11.079745625}Solution
x = {14.079745625, -11.079745625}
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