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Simplifying (6x + 3)(42 + -1x) = 90 Reorder the terms: (3 + 6x)(42 + -1x) = 90 Multiply (3 + 6x) * (42 + -1x) (3(42 + -1x) + 6x * (42 + -1x)) = 90 ((42 * 3 + -1x * 3) + 6x * (42 + -1x)) = 90 ((126 + -3x) + 6x * (42 + -1x)) = 90 (126 + -3x + (42 * 6x + -1x * 6x)) = 90 (126 + -3x + (252x + -6x2)) = 90 Combine like terms: -3x + 252x = 249x (126 + 249x + -6x2) = 90 Solving 126 + 249x + -6x2 = 90 Solving for variable 'x'. Reorder the terms: 126 + -90 + 249x + -6x2 = 90 + -90 Combine like terms: 126 + -90 = 36 36 + 249x + -6x2 = 90 + -90 Combine like terms: 90 + -90 = 0 36 + 249x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(12 + 83x + -2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(12 + 83x + -2x2)' equal to zero and attempt to solve: Simplifying 12 + 83x + -2x2 = 0 Solving 12 + 83x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -6 + -41.5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -41.5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -41.5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -41.5x + x2 = 0 + 6 -41.5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -41.5x + x2 = 6 The x term is -41.5x. Take half its coefficient (-20.75). Square it (430.5625) and add it to both sides. Add '430.5625' to each side of the equation. -41.5x + 430.5625 + x2 = 6 + 430.5625 Reorder the terms: 430.5625 + -41.5x + x2 = 6 + 430.5625 Combine like terms: 6 + 430.5625 = 436.5625 430.5625 + -41.5x + x2 = 436.5625 Factor a perfect square on the left side: (x + -20.75)(x + -20.75) = 436.5625 Calculate the square root of the right side: 20.894078108 Break this problem into two subproblems by setting (x + -20.75) equal to 20.894078108 and -20.894078108.Subproblem 1
x + -20.75 = 20.894078108 Simplifying x + -20.75 = 20.894078108 Reorder the terms: -20.75 + x = 20.894078108 Solving -20.75 + x = 20.894078108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.75' to each side of the equation. -20.75 + 20.75 + x = 20.894078108 + 20.75 Combine like terms: -20.75 + 20.75 = 0.00 0.00 + x = 20.894078108 + 20.75 x = 20.894078108 + 20.75 Combine like terms: 20.894078108 + 20.75 = 41.644078108 x = 41.644078108 Simplifying x = 41.644078108Subproblem 2
x + -20.75 = -20.894078108 Simplifying x + -20.75 = -20.894078108 Reorder the terms: -20.75 + x = -20.894078108 Solving -20.75 + x = -20.894078108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.75' to each side of the equation. -20.75 + 20.75 + x = -20.894078108 + 20.75 Combine like terms: -20.75 + 20.75 = 0.00 0.00 + x = -20.894078108 + 20.75 x = -20.894078108 + 20.75 Combine like terms: -20.894078108 + 20.75 = -0.144078108 x = -0.144078108 Simplifying x = -0.144078108Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.644078108, -0.144078108}Solution
x = {41.644078108, -0.144078108}
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