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Simplifying (2x + 2)(3x + 6) + -4 = 0 Reorder the terms: (2 + 2x)(3x + 6) + -4 = 0 Reorder the terms: (2 + 2x)(6 + 3x) + -4 = 0 Multiply (2 + 2x) * (6 + 3x) (2(6 + 3x) + 2x * (6 + 3x)) + -4 = 0 ((6 * 2 + 3x * 2) + 2x * (6 + 3x)) + -4 = 0 ((12 + 6x) + 2x * (6 + 3x)) + -4 = 0 (12 + 6x + (6 * 2x + 3x * 2x)) + -4 = 0 (12 + 6x + (12x + 6x2)) + -4 = 0 Combine like terms: 6x + 12x = 18x (12 + 18x + 6x2) + -4 = 0 Reorder the terms: 12 + -4 + 18x + 6x2 = 0 Combine like terms: 12 + -4 = 8 8 + 18x + 6x2 = 0 Solving 8 + 18x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 9x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 9x + 3x2)' equal to zero and attempt to solve: Simplifying 4 + 9x + 3x2 = 0 Solving 4 + 9x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + 3x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 3x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 3x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 3x + x2 = 0 + -1.333333333 3x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 3x + x2 = -1.333333333 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 = -1.333333333 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -1.333333333 + 2.25 Combine like terms: -1.333333333 + 2.25 = 0.916666667 2.25 + 3x + x2 = 0.916666667 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 0.916666667 Calculate the square root of the right side: 0.957427108 Break this problem into two subproblems by setting (x + 1.5) equal to 0.957427108 and -0.957427108.Subproblem 1
x + 1.5 = 0.957427108 Simplifying x + 1.5 = 0.957427108 Reorder the terms: 1.5 + x = 0.957427108 Solving 1.5 + x = 0.957427108 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 = 0.957427108 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 0.957427108 + -1.5 x = 0.957427108 + -1.5 Combine like terms: 0.957427108 + -1.5 = -0.542572892 x = -0.542572892 Simplifying x = -0.542572892Subproblem 2
x + 1.5 = -0.957427108 Simplifying x + 1.5 = -0.957427108 Reorder the terms: 1.5 + x = -0.957427108 Solving 1.5 + x = -0.957427108 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 = -0.957427108 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -0.957427108 + -1.5 x = -0.957427108 + -1.5 Combine like terms: -0.957427108 + -1.5 = -2.457427108 x = -2.457427108 Simplifying x = -2.457427108Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.542572892, -2.457427108}Solution
x = {-0.542572892, -2.457427108}
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