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Simplifying (3x + 3)(5x + -2) = 12 Reorder the terms: (3 + 3x)(5x + -2) = 12 Reorder the terms: (3 + 3x)(-2 + 5x) = 12 Multiply (3 + 3x) * (-2 + 5x) (3(-2 + 5x) + 3x * (-2 + 5x)) = 12 ((-2 * 3 + 5x * 3) + 3x * (-2 + 5x)) = 12 ((-6 + 15x) + 3x * (-2 + 5x)) = 12 (-6 + 15x + (-2 * 3x + 5x * 3x)) = 12 (-6 + 15x + (-6x + 15x2)) = 12 Combine like terms: 15x + -6x = 9x (-6 + 9x + 15x2) = 12 Solving -6 + 9x + 15x2 = 12 Solving for variable 'x'. Reorder the terms: -6 + -12 + 9x + 15x2 = 12 + -12 Combine like terms: -6 + -12 = -18 -18 + 9x + 15x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -18 + 9x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + 3x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-6 + 3x + 5x2)' equal to zero and attempt to solve: Simplifying -6 + 3x + 5x2 = 0 Solving -6 + 3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + 0.6x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 0.6x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 0.6x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 0.6x + x2 = 0 + 1.2 0.6x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 0.6x + x2 = 1.2 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 1.2 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 1.2 + 0.09 Combine like terms: 1.2 + 0.09 = 1.29 0.09 + 0.6x + x2 = 1.29 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 1.29 Calculate the square root of the right side: 1.135781669 Break this problem into two subproblems by setting (x + 0.3) equal to 1.135781669 and -1.135781669.Subproblem 1
x + 0.3 = 1.135781669 Simplifying x + 0.3 = 1.135781669 Reorder the terms: 0.3 + x = 1.135781669 Solving 0.3 + x = 1.135781669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 1.135781669 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 1.135781669 + -0.3 x = 1.135781669 + -0.3 Combine like terms: 1.135781669 + -0.3 = 0.835781669 x = 0.835781669 Simplifying x = 0.835781669Subproblem 2
x + 0.3 = -1.135781669 Simplifying x + 0.3 = -1.135781669 Reorder the terms: 0.3 + x = -1.135781669 Solving 0.3 + x = -1.135781669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -1.135781669 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -1.135781669 + -0.3 x = -1.135781669 + -0.3 Combine like terms: -1.135781669 + -0.3 = -1.435781669 x = -1.435781669 Simplifying x = -1.435781669Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.835781669, -1.435781669}Solution
x = {0.835781669, -1.435781669}
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