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Simplifying (2x + 4)(3x + 3) = 22 Reorder the terms: (4 + 2x)(3x + 3) = 22 Reorder the terms: (4 + 2x)(3 + 3x) = 22 Multiply (4 + 2x) * (3 + 3x) (4(3 + 3x) + 2x * (3 + 3x)) = 22 ((3 * 4 + 3x * 4) + 2x * (3 + 3x)) = 22 ((12 + 12x) + 2x * (3 + 3x)) = 22 (12 + 12x + (3 * 2x + 3x * 2x)) = 22 (12 + 12x + (6x + 6x2)) = 22 Combine like terms: 12x + 6x = 18x (12 + 18x + 6x2) = 22 Solving 12 + 18x + 6x2 = 22 Solving for variable 'x'. Reorder the terms: 12 + -22 + 18x + 6x2 = 22 + -22 Combine like terms: 12 + -22 = -10 -10 + 18x + 6x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -10 + 18x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 9x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 9x + 3x2)' equal to zero and attempt to solve: Simplifying -5 + 9x + 3x2 = 0 Solving -5 + 9x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.666666667 + 3x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + 3x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + 3x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + 3x + x2 = 0 + 1.666666667 3x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 3x + x2 = 1.666666667 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 = 1.666666667 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 1.666666667 + 2.25 Combine like terms: 1.666666667 + 2.25 = 3.916666667 2.25 + 3x + x2 = 3.916666667 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 3.916666667 Calculate the square root of the right side: 1.979057015 Break this problem into two subproblems by setting (x + 1.5) equal to 1.979057015 and -1.979057015.Subproblem 1
x + 1.5 = 1.979057015 Simplifying x + 1.5 = 1.979057015 Reorder the terms: 1.5 + x = 1.979057015 Solving 1.5 + x = 1.979057015 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 = 1.979057015 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.979057015 + -1.5 x = 1.979057015 + -1.5 Combine like terms: 1.979057015 + -1.5 = 0.479057015 x = 0.479057015 Simplifying x = 0.479057015Subproblem 2
x + 1.5 = -1.979057015 Simplifying x + 1.5 = -1.979057015 Reorder the terms: 1.5 + x = -1.979057015 Solving 1.5 + x = -1.979057015 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 = -1.979057015 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.979057015 + -1.5 x = -1.979057015 + -1.5 Combine like terms: -1.979057015 + -1.5 = -3.479057015 x = -3.479057015 Simplifying x = -3.479057015Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.479057015, -3.479057015}Solution
x = {0.479057015, -3.479057015}
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