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Simplifying 6x2 + -12x + -78 = 0 Reorder the terms: -78 + -12x + 6x2 = 0 Solving -78 + -12x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-13 + -2x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-13 + -2x + x2)' equal to zero and attempt to solve: Simplifying -13 + -2x + x2 = 0 Solving -13 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -2x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -2x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -2x + x2 = 0 + 13 -2x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -2x + x2 = 13 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 = 13 + 1 Reorder the terms: 1 + -2x + x2 = 13 + 1 Combine like terms: 13 + 1 = 14 1 + -2x + x2 = 14 Factor a perfect square on the left side: (x + -1)(x + -1) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + -1) equal to 3.741657387 and -3.741657387.Subproblem 1
x + -1 = 3.741657387 Simplifying x + -1 = 3.741657387 Reorder the terms: -1 + x = 3.741657387 Solving -1 + x = 3.741657387 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 = 3.741657387 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.741657387 + 1 x = 3.741657387 + 1 Combine like terms: 3.741657387 + 1 = 4.741657387 x = 4.741657387 Simplifying x = 4.741657387Subproblem 2
x + -1 = -3.741657387 Simplifying x + -1 = -3.741657387 Reorder the terms: -1 + x = -3.741657387 Solving -1 + x = -3.741657387 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 = -3.741657387 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.741657387 + 1 x = -3.741657387 + 1 Combine like terms: -3.741657387 + 1 = -2.741657387 x = -2.741657387 Simplifying x = -2.741657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.741657387, -2.741657387}Solution
x = {4.741657387, -2.741657387}
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