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Simplifying 20x + (17x + 7) + 15x(12x + 17) = 360 Reorder the terms: 20x + (7 + 17x) + 15x(12x + 17) = 360 Remove parenthesis around (7 + 17x) 20x + 7 + 17x + 15x(12x + 17) = 360 Reorder the terms: 20x + 7 + 17x + 15x(17 + 12x) = 360 20x + 7 + 17x + (17 * 15x + 12x * 15x) = 360 20x + 7 + 17x + (255x + 180x2) = 360 Reorder the terms: 7 + 20x + 17x + 255x + 180x2 = 360 Combine like terms: 20x + 17x = 37x 7 + 37x + 255x + 180x2 = 360 Combine like terms: 37x + 255x = 292x 7 + 292x + 180x2 = 360 Solving 7 + 292x + 180x2 = 360 Solving for variable 'x'. Reorder the terms: 7 + -360 + 292x + 180x2 = 360 + -360 Combine like terms: 7 + -360 = -353 -353 + 292x + 180x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -353 + 292x + 180x2 = 0 Begin completing the square. Divide all terms by 180 the coefficient of the squared term: Divide each side by '180'. -1.961111111 + 1.622222222x + x2 = 0.0 Move the constant term to the right: Add '1.961111111' to each side of the equation. -1.961111111 + 1.622222222x + 1.961111111 + x2 = 0.0 + 1.961111111 Reorder the terms: -1.961111111 + 1.961111111 + 1.622222222x + x2 = 0.0 + 1.961111111 Combine like terms: -1.961111111 + 1.961111111 = 0.000000000 0.000000000 + 1.622222222x + x2 = 0.0 + 1.961111111 1.622222222x + x2 = 0.0 + 1.961111111 Combine like terms: 0.0 + 1.961111111 = 1.961111111 1.622222222x + x2 = 1.961111111 The x term is 1.622222222x. Take half its coefficient (0.811111111). Square it (0.6579012344) and add it to both sides. Add '0.6579012344' to each side of the equation. 1.622222222x + 0.6579012344 + x2 = 1.961111111 + 0.6579012344 Reorder the terms: 0.6579012344 + 1.622222222x + x2 = 1.961111111 + 0.6579012344 Combine like terms: 1.961111111 + 0.6579012344 = 2.6190123454 0.6579012344 + 1.622222222x + x2 = 2.6190123454 Factor a perfect square on the left side: (x + 0.811111111)(x + 0.811111111) = 2.6190123454 Calculate the square root of the right side: 1.618336289 Break this problem into two subproblems by setting (x + 0.811111111) equal to 1.618336289 and -1.618336289.Subproblem 1
x + 0.811111111 = 1.618336289 Simplifying x + 0.811111111 = 1.618336289 Reorder the terms: 0.811111111 + x = 1.618336289 Solving 0.811111111 + x = 1.618336289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.811111111' to each side of the equation. 0.811111111 + -0.811111111 + x = 1.618336289 + -0.811111111 Combine like terms: 0.811111111 + -0.811111111 = 0.000000000 0.000000000 + x = 1.618336289 + -0.811111111 x = 1.618336289 + -0.811111111 Combine like terms: 1.618336289 + -0.811111111 = 0.807225178 x = 0.807225178 Simplifying x = 0.807225178Subproblem 2
x + 0.811111111 = -1.618336289 Simplifying x + 0.811111111 = -1.618336289 Reorder the terms: 0.811111111 + x = -1.618336289 Solving 0.811111111 + x = -1.618336289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.811111111' to each side of the equation. 0.811111111 + -0.811111111 + x = -1.618336289 + -0.811111111 Combine like terms: 0.811111111 + -0.811111111 = 0.000000000 0.000000000 + x = -1.618336289 + -0.811111111 x = -1.618336289 + -0.811111111 Combine like terms: -1.618336289 + -0.811111111 = -2.4294474 x = -2.4294474 Simplifying x = -2.4294474Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.807225178, -2.4294474}
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