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Simplifying (2x + -6)(2x + -6) = 38 Reorder the terms: (-6 + 2x)(2x + -6) = 38 Reorder the terms: (-6 + 2x)(-6 + 2x) = 38 Multiply (-6 + 2x) * (-6 + 2x) (-6(-6 + 2x) + 2x * (-6 + 2x)) = 38 ((-6 * -6 + 2x * -6) + 2x * (-6 + 2x)) = 38 ((36 + -12x) + 2x * (-6 + 2x)) = 38 (36 + -12x + (-6 * 2x + 2x * 2x)) = 38 (36 + -12x + (-12x + 4x2)) = 38 Combine like terms: -12x + -12x = -24x (36 + -24x + 4x2) = 38 Solving 36 + -24x + 4x2 = 38 Solving for variable 'x'. Reorder the terms: 36 + -38 + -24x + 4x2 = 38 + -38 Combine like terms: 36 + -38 = -2 -2 + -24x + 4x2 = 38 + -38 Combine like terms: 38 + -38 = 0 -2 + -24x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -12x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -12x + 2x2)' equal to zero and attempt to solve: Simplifying -1 + -12x + 2x2 = 0 Solving -1 + -12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -6x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -6x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -6x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -6x + x2 = 0 + 0.5 -6x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -6x + x2 = 0.5 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 0.5 + 9 Reorder the terms: 9 + -6x + x2 = 0.5 + 9 Combine like terms: 0.5 + 9 = 9.5 9 + -6x + x2 = 9.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (x + -3) equal to 3.082207001 and -3.082207001.Subproblem 1
x + -3 = 3.082207001 Simplifying x + -3 = 3.082207001 Reorder the terms: -3 + x = 3.082207001 Solving -3 + x = 3.082207001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.082207001 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.082207001 + 3 x = 3.082207001 + 3 Combine like terms: 3.082207001 + 3 = 6.082207001 x = 6.082207001 Simplifying x = 6.082207001Subproblem 2
x + -3 = -3.082207001 Simplifying x + -3 = -3.082207001 Reorder the terms: -3 + x = -3.082207001 Solving -3 + x = -3.082207001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.082207001 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.082207001 + 3 x = -3.082207001 + 3 Combine like terms: -3.082207001 + 3 = -0.082207001 x = -0.082207001 Simplifying x = -0.082207001Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.082207001, -0.082207001}Solution
x = {6.082207001, -0.082207001}
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