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Simplifying 6x2 + -12x + -93 = -9 Reorder the terms: -93 + -12x + 6x2 = -9 Solving -93 + -12x + 6x2 = -9 Solving for variable 'x'. Reorder the terms: -93 + 9 + -12x + 6x2 = -9 + 9 Combine like terms: -93 + 9 = -84 -84 + -12x + 6x2 = -9 + 9 Combine like terms: -9 + 9 = 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 = 4.872983346 x = 4.872983346 Simplifying x = 4.872983346Subproblem 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 = -2.872983346 x = -2.872983346 Simplifying x = -2.872983346Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.872983346, -2.872983346}Solution
x = {4.872983346, -2.872983346}
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