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Simplifying 136 = (2x + 2)(x + 2) Reorder the terms: 136 = (2 + 2x)(x + 2) Reorder the terms: 136 = (2 + 2x)(2 + x) Multiply (2 + 2x) * (2 + x) 136 = (2(2 + x) + 2x * (2 + x)) 136 = ((2 * 2 + x * 2) + 2x * (2 + x)) 136 = ((4 + 2x) + 2x * (2 + x)) 136 = (4 + 2x + (2 * 2x + x * 2x)) 136 = (4 + 2x + (4x + 2x2)) Combine like terms: 2x + 4x = 6x 136 = (4 + 6x + 2x2) Solving 136 = 4 + 6x + 2x2 Solving for variable 'x'. Combine like terms: 136 + -4 = 132 132 + -6x + -2x2 = 4 + 6x + 2x2 + -4 + -6x + -2x2 Reorder the terms: 132 + -6x + -2x2 = 4 + -4 + 6x + -6x + 2x2 + -2x2 Combine like terms: 4 + -4 = 0 132 + -6x + -2x2 = 0 + 6x + -6x + 2x2 + -2x2 132 + -6x + -2x2 = 6x + -6x + 2x2 + -2x2 Combine like terms: 6x + -6x = 0 132 + -6x + -2x2 = 0 + 2x2 + -2x2 132 + -6x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 132 + -6x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(66 + -3x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(66 + -3x + -1x2)' equal to zero and attempt to solve: Simplifying 66 + -3x + -1x2 = 0 Solving 66 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -66 + 3x + x2 = 0 Move the constant term to the right: Add '66' to each side of the equation. -66 + 3x + 66 + x2 = 0 + 66 Reorder the terms: -66 + 66 + 3x + x2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + 3x + x2 = 0 + 66 3x + x2 = 0 + 66 Combine like terms: 0 + 66 = 66 3x + x2 = 66 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 = 66 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 66 + 2.25 Combine like terms: 66 + 2.25 = 68.25 2.25 + 3x + x2 = 68.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 68.25 Calculate the square root of the right side: 8.261355821 Break this problem into two subproblems by setting (x + 1.5) equal to 8.261355821 and -8.261355821.Subproblem 1
x + 1.5 = 8.261355821 Simplifying x + 1.5 = 8.261355821 Reorder the terms: 1.5 + x = 8.261355821 Solving 1.5 + x = 8.261355821 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 = 8.261355821 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 8.261355821 + -1.5 x = 8.261355821 + -1.5 Combine like terms: 8.261355821 + -1.5 = 6.761355821 x = 6.761355821 Simplifying x = 6.761355821Subproblem 2
x + 1.5 = -8.261355821 Simplifying x + 1.5 = -8.261355821 Reorder the terms: 1.5 + x = -8.261355821 Solving 1.5 + x = -8.261355821 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 = -8.261355821 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -8.261355821 + -1.5 x = -8.261355821 + -1.5 Combine like terms: -8.261355821 + -1.5 = -9.761355821 x = -9.761355821 Simplifying x = -9.761355821Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.761355821, -9.761355821}Solution
x = {6.761355821, -9.761355821}
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