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Simplifying (x + 2)(3x + 3) = 5 Reorder the terms: (2 + x)(3x + 3) = 5 Reorder the terms: (2 + x)(3 + 3x) = 5 Multiply (2 + x) * (3 + 3x) (2(3 + 3x) + x(3 + 3x)) = 5 ((3 * 2 + 3x * 2) + x(3 + 3x)) = 5 ((6 + 6x) + x(3 + 3x)) = 5 (6 + 6x + (3 * x + 3x * x)) = 5 (6 + 6x + (3x + 3x2)) = 5 Combine like terms: 6x + 3x = 9x (6 + 9x + 3x2) = 5 Solving 6 + 9x + 3x2 = 5 Solving for variable 'x'. Reorder the terms: 6 + -5 + 9x + 3x2 = 5 + -5 Combine like terms: 6 + -5 = 1 1 + 9x + 3x2 = 5 + -5 Combine like terms: 5 + -5 = 0 1 + 9x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + 3x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 3x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 3x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 3x + x2 = 0 + -0.3333333333 3x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 3x + x2 = -0.3333333333 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 = -0.3333333333 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -0.3333333333 + 2.25 Combine like terms: -0.3333333333 + 2.25 = 1.9166666667 2.25 + 3x + x2 = 1.9166666667 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 1.9166666667 Calculate the square root of the right side: 1.38443731 Break this problem into two subproblems by setting (x + 1.5) equal to 1.38443731 and -1.38443731.Subproblem 1
x + 1.5 = 1.38443731 Simplifying x + 1.5 = 1.38443731 Reorder the terms: 1.5 + x = 1.38443731 Solving 1.5 + x = 1.38443731 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 = 1.38443731 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.38443731 + -1.5 x = 1.38443731 + -1.5 Combine like terms: 1.38443731 + -1.5 = -0.11556269 x = -0.11556269 Simplifying x = -0.11556269Subproblem 2
x + 1.5 = -1.38443731 Simplifying x + 1.5 = -1.38443731 Reorder the terms: 1.5 + x = -1.38443731 Solving 1.5 + x = -1.38443731 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 = -1.38443731 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.38443731 + -1.5 x = -1.38443731 + -1.5 Combine like terms: -1.38443731 + -1.5 = -2.88443731 x = -2.88443731 Simplifying x = -2.88443731Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.11556269, -2.88443731}
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