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Simplifying (x + 15)(3x + -17) = 90 Reorder the terms: (15 + x)(3x + -17) = 90 Reorder the terms: (15 + x)(-17 + 3x) = 90 Multiply (15 + x) * (-17 + 3x) (15(-17 + 3x) + x(-17 + 3x)) = 90 ((-17 * 15 + 3x * 15) + x(-17 + 3x)) = 90 ((-255 + 45x) + x(-17 + 3x)) = 90 (-255 + 45x + (-17 * x + 3x * x)) = 90 (-255 + 45x + (-17x + 3x2)) = 90 Combine like terms: 45x + -17x = 28x (-255 + 28x + 3x2) = 90 Solving -255 + 28x + 3x2 = 90 Solving for variable 'x'. Reorder the terms: -255 + -90 + 28x + 3x2 = 90 + -90 Combine like terms: -255 + -90 = -345 -345 + 28x + 3x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -345 + 28x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -115 + 9.333333333x + x2 = 0 Move the constant term to the right: Add '115' to each side of the equation. -115 + 9.333333333x + 115 + x2 = 0 + 115 Reorder the terms: -115 + 115 + 9.333333333x + x2 = 0 + 115 Combine like terms: -115 + 115 = 0 0 + 9.333333333x + x2 = 0 + 115 9.333333333x + x2 = 0 + 115 Combine like terms: 0 + 115 = 115 9.333333333x + x2 = 115 The x term is 9.333333333x. Take half its coefficient (4.666666667). Square it (21.77777778) and add it to both sides. Add '21.77777778' to each side of the equation. 9.333333333x + 21.77777778 + x2 = 115 + 21.77777778 Reorder the terms: 21.77777778 + 9.333333333x + x2 = 115 + 21.77777778 Combine like terms: 115 + 21.77777778 = 136.77777778 21.77777778 + 9.333333333x + x2 = 136.77777778 Factor a perfect square on the left side: (x + 4.666666667)(x + 4.666666667) = 136.77777778 Calculate the square root of the right side: 11.695203195 Break this problem into two subproblems by setting (x + 4.666666667) equal to 11.695203195 and -11.695203195.Subproblem 1
x + 4.666666667 = 11.695203195 Simplifying x + 4.666666667 = 11.695203195 Reorder the terms: 4.666666667 + x = 11.695203195 Solving 4.666666667 + x = 11.695203195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.666666667' to each side of the equation. 4.666666667 + -4.666666667 + x = 11.695203195 + -4.666666667 Combine like terms: 4.666666667 + -4.666666667 = 0.000000000 0.000000000 + x = 11.695203195 + -4.666666667 x = 11.695203195 + -4.666666667 Combine like terms: 11.695203195 + -4.666666667 = 7.028536528 x = 7.028536528 Simplifying x = 7.028536528Subproblem 2
x + 4.666666667 = -11.695203195 Simplifying x + 4.666666667 = -11.695203195 Reorder the terms: 4.666666667 + x = -11.695203195 Solving 4.666666667 + x = -11.695203195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.666666667' to each side of the equation. 4.666666667 + -4.666666667 + x = -11.695203195 + -4.666666667 Combine like terms: 4.666666667 + -4.666666667 = 0.000000000 0.000000000 + x = -11.695203195 + -4.666666667 x = -11.695203195 + -4.666666667 Combine like terms: -11.695203195 + -4.666666667 = -16.361869862 x = -16.361869862 Simplifying x = -16.361869862Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.028536528, -16.361869862}
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