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Simplifying 3x + -17(x + 40)(2x + -5) = 180 Reorder the terms: 3x + -17(40 + x)(2x + -5) = 180 Reorder the terms: 3x + -17(40 + x)(-5 + 2x) = 180 Multiply (40 + x) * (-5 + 2x) 3x + -17(40(-5 + 2x) + x(-5 + 2x)) = 180 3x + -17((-5 * 40 + 2x * 40) + x(-5 + 2x)) = 180 3x + -17((-200 + 80x) + x(-5 + 2x)) = 180 3x + -17(-200 + 80x + (-5 * x + 2x * x)) = 180 3x + -17(-200 + 80x + (-5x + 2x2)) = 180 Combine like terms: 80x + -5x = 75x 3x + -17(-200 + 75x + 2x2) = 180 3x + (-200 * -17 + 75x * -17 + 2x2 * -17) = 180 3x + (3400 + -1275x + -34x2) = 180 Reorder the terms: 3400 + 3x + -1275x + -34x2 = 180 Combine like terms: 3x + -1275x = -1272x 3400 + -1272x + -34x2 = 180 Solving 3400 + -1272x + -34x2 = 180 Solving for variable 'x'. Reorder the terms: 3400 + -180 + -1272x + -34x2 = 180 + -180 Combine like terms: 3400 + -180 = 3220 3220 + -1272x + -34x2 = 180 + -180 Combine like terms: 180 + -180 = 0 3220 + -1272x + -34x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1610 + -636x + -17x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1610 + -636x + -17x2)' equal to zero and attempt to solve: Simplifying 1610 + -636x + -17x2 = 0 Solving 1610 + -636x + -17x2 = 0 Begin completing the square. Divide all terms by -17 the coefficient of the squared term: Divide each side by '-17'. -94.70588235 + 37.41176471x + x2 = 0 Move the constant term to the right: Add '94.70588235' to each side of the equation. -94.70588235 + 37.41176471x + 94.70588235 + x2 = 0 + 94.70588235 Reorder the terms: -94.70588235 + 94.70588235 + 37.41176471x + x2 = 0 + 94.70588235 Combine like terms: -94.70588235 + 94.70588235 = 0.00000000 0.00000000 + 37.41176471x + x2 = 0 + 94.70588235 37.41176471x + x2 = 0 + 94.70588235 Combine like terms: 0 + 94.70588235 = 94.70588235 37.41176471x + x2 = 94.70588235 The x term is 37.41176471x. Take half its coefficient (18.70588236). Square it (349.9100349) and add it to both sides. Add '349.9100349' to each side of the equation. 37.41176471x + 349.9100349 + x2 = 94.70588235 + 349.9100349 Reorder the terms: 349.9100349 + 37.41176471x + x2 = 94.70588235 + 349.9100349 Combine like terms: 94.70588235 + 349.9100349 = 444.61591725 349.9100349 + 37.41176471x + x2 = 444.61591725 Factor a perfect square on the left side: (x + 18.70588236)(x + 18.70588236) = 444.61591725 Calculate the square root of the right side: 21.08591751 Break this problem into two subproblems by setting (x + 18.70588236) equal to 21.08591751 and -21.08591751.Subproblem 1
x + 18.70588236 = 21.08591751 Simplifying x + 18.70588236 = 21.08591751 Reorder the terms: 18.70588236 + x = 21.08591751 Solving 18.70588236 + x = 21.08591751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.70588236' to each side of the equation. 18.70588236 + -18.70588236 + x = 21.08591751 + -18.70588236 Combine like terms: 18.70588236 + -18.70588236 = 0.00000000 0.00000000 + x = 21.08591751 + -18.70588236 x = 21.08591751 + -18.70588236 Combine like terms: 21.08591751 + -18.70588236 = 2.38003515 x = 2.38003515 Simplifying x = 2.38003515Subproblem 2
x + 18.70588236 = -21.08591751 Simplifying x + 18.70588236 = -21.08591751 Reorder the terms: 18.70588236 + x = -21.08591751 Solving 18.70588236 + x = -21.08591751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.70588236' to each side of the equation. 18.70588236 + -18.70588236 + x = -21.08591751 + -18.70588236 Combine like terms: 18.70588236 + -18.70588236 = 0.00000000 0.00000000 + x = -21.08591751 + -18.70588236 x = -21.08591751 + -18.70588236 Combine like terms: -21.08591751 + -18.70588236 = -39.79179987 x = -39.79179987 Simplifying x = -39.79179987Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.38003515, -39.79179987}Solution
x = {2.38003515, -39.79179987}
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