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Simplifying 6x2 + 12x + 32 = 116 Reorder the terms: 32 + 12x + 6x2 = 116 Solving 32 + 12x + 6x2 = 116 Solving for variable 'x'. Reorder the terms: 32 + -116 + 12x + 6x2 = 116 + -116 Combine like terms: 32 + -116 = -84 -84 + 12x + 6x2 = 116 + -116 Combine like terms: 116 + -116 = 0 -84 + 12x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-14 + 2x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-14 + 2x + x2)' equal to zero and attempt to solve: Simplifying -14 + 2x + x2 = 0 Solving -14 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 2x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 2x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 2x + x2 = 0 + 14 2x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 2x + x2 = 14 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 = 14 + 1 Reorder the terms: 1 + 2x + x2 = 14 + 1 Combine like terms: 14 + 1 = 15 1 + 2x + x2 = 15 Factor a perfect square on the left side: (x + 1)(x + 1) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + 1) equal to 3.872983346 and -3.872983346.Subproblem 1
x + 1 = 3.872983346 Simplifying x + 1 = 3.872983346 Reorder the terms: 1 + x = 3.872983346 Solving 1 + x = 3.872983346 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 = 3.872983346 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.872983346 + -1 x = 3.872983346 + -1 Combine like terms: 3.872983346 + -1 = 2.872983346 x = 2.872983346 Simplifying x = 2.872983346Subproblem 2
x + 1 = -3.872983346 Simplifying x + 1 = -3.872983346 Reorder the terms: 1 + x = -3.872983346 Solving 1 + x = -3.872983346 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 = -3.872983346 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.872983346 + -1 x = -3.872983346 + -1 Combine like terms: -3.872983346 + -1 = -4.872983346 x = -4.872983346 Simplifying x = -4.872983346Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.872983346, -4.872983346}Solution
x = {2.872983346, -4.872983346}
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