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Simplifying (3x)(12) + -1(5) = (2x)(15x) + -20 Remove parenthesis around (3x) 3x(12) + -1(5) = (2x)(15x) + -20 Reorder the terms for easier multiplication: 3 * 12x + -1(5) = (2x)(15x) + -20 Multiply 3 * 12 36x + -1(5) = (2x)(15x) + -20 Multiply -1 * 5 36x + -5 = (2x)(15x) + -20 Reorder the terms: -5 + 36x = (2x)(15x) + -20 Remove parenthesis around (2x) -5 + 36x = 2x(15x) + -20 Remove parenthesis around (15x) -5 + 36x = 2x * 15x + -20 Reorder the terms for easier multiplication: -5 + 36x = 2 * 15x * x + -20 Multiply 2 * 15 -5 + 36x = 30x * x + -20 Multiply x * x -5 + 36x = 30x2 + -20 Reorder the terms: -5 + 36x = -20 + 30x2 Solving -5 + 36x = -20 + 30x2 Solving for variable 'x'. Reorder the terms: -5 + 20 + 36x + -30x2 = -20 + 30x2 + 20 + -30x2 Combine like terms: -5 + 20 = 15 15 + 36x + -30x2 = -20 + 30x2 + 20 + -30x2 Reorder the terms: 15 + 36x + -30x2 = -20 + 20 + 30x2 + -30x2 Combine like terms: -20 + 20 = 0 15 + 36x + -30x2 = 0 + 30x2 + -30x2 15 + 36x + -30x2 = 30x2 + -30x2 Combine like terms: 30x2 + -30x2 = 0 15 + 36x + -30x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(5 + 12x + -10x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + 12x + -10x2)' equal to zero and attempt to solve: Simplifying 5 + 12x + -10x2 = 0 Solving 5 + 12x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.5 + -1.2x + x2 = 0.0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -1.2x + 0.5 + x2 = 0.0 + 0.5 Reorder the terms: -0.5 + 0.5 + -1.2x + x2 = 0.0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -1.2x + x2 = 0.0 + 0.5 -1.2x + x2 = 0.0 + 0.5 Combine like terms: 0.0 + 0.5 = 0.5 -1.2x + x2 = 0.5 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 0.5 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 0.5 + 0.36 Combine like terms: 0.5 + 0.36 = 0.86 0.36 + -1.2x + x2 = 0.86 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 0.86 Calculate the square root of the right side: 0.92736185 Break this problem into two subproblems by setting (x + -0.6) equal to 0.92736185 and -0.92736185.Subproblem 1
x + -0.6 = 0.92736185 Simplifying x + -0.6 = 0.92736185 Reorder the terms: -0.6 + x = 0.92736185 Solving -0.6 + x = 0.92736185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 0.92736185 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.92736185 + 0.6 x = 0.92736185 + 0.6 Combine like terms: 0.92736185 + 0.6 = 1.52736185 x = 1.52736185 Simplifying x = 1.52736185Subproblem 2
x + -0.6 = -0.92736185 Simplifying x + -0.6 = -0.92736185 Reorder the terms: -0.6 + x = -0.92736185 Solving -0.6 + x = -0.92736185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -0.92736185 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.92736185 + 0.6 x = -0.92736185 + 0.6 Combine like terms: -0.92736185 + 0.6 = -0.32736185 x = -0.32736185 Simplifying x = -0.32736185Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.52736185, -0.32736185}Solution
x = {1.52736185, -0.32736185}
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