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Simplifying (x + 5) + (x + 10) + (x + 15)(x + 20) = 153 Reorder the terms: (5 + x) + (x + 10) + (x + 15)(x + 20) = 153 Remove parenthesis around (5 + x) 5 + x + (x + 10) + (x + 15)(x + 20) = 153 Reorder the terms: 5 + x + (10 + x) + (x + 15)(x + 20) = 153 Remove parenthesis around (10 + x) 5 + x + 10 + x + (x + 15)(x + 20) = 153 Reorder the terms: 5 + x + 10 + x + (15 + x)(x + 20) = 153 Reorder the terms: 5 + x + 10 + x + (15 + x)(20 + x) = 153 Multiply (15 + x) * (20 + x) 5 + x + 10 + x + (15(20 + x) + x(20 + x)) = 153 5 + x + 10 + x + ((20 * 15 + x * 15) + x(20 + x)) = 153 5 + x + 10 + x + ((300 + 15x) + x(20 + x)) = 153 5 + x + 10 + x + (300 + 15x + (20 * x + x * x)) = 153 5 + x + 10 + x + (300 + 15x + (20x + x2)) = 153 Combine like terms: 15x + 20x = 35x 5 + x + 10 + x + (300 + 35x + x2) = 153 Reorder the terms: 5 + 10 + 300 + x + x + 35x + x2 = 153 Combine like terms: 5 + 10 = 15 15 + 300 + x + x + 35x + x2 = 153 Combine like terms: 15 + 300 = 315 315 + x + x + 35x + x2 = 153 Combine like terms: x + x = 2x 315 + 2x + 35x + x2 = 153 Combine like terms: 2x + 35x = 37x 315 + 37x + x2 = 153 Solving 315 + 37x + x2 = 153 Solving for variable 'x'. Reorder the terms: 315 + -153 + 37x + x2 = 153 + -153 Combine like terms: 315 + -153 = 162 162 + 37x + x2 = 153 + -153 Combine like terms: 153 + -153 = 0 162 + 37x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-162' to each side of the equation. 162 + 37x + -162 + x2 = 0 + -162 Reorder the terms: 162 + -162 + 37x + x2 = 0 + -162 Combine like terms: 162 + -162 = 0 0 + 37x + x2 = 0 + -162 37x + x2 = 0 + -162 Combine like terms: 0 + -162 = -162 37x + x2 = -162 The x term is 37x. Take half its coefficient (18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. 37x + 342.25 + x2 = -162 + 342.25 Reorder the terms: 342.25 + 37x + x2 = -162 + 342.25 Combine like terms: -162 + 342.25 = 180.25 342.25 + 37x + x2 = 180.25 Factor a perfect square on the left side: (x + 18.5)(x + 18.5) = 180.25 Calculate the square root of the right side: 13.425721582 Break this problem into two subproblems by setting (x + 18.5) equal to 13.425721582 and -13.425721582.Subproblem 1
x + 18.5 = 13.425721582 Simplifying x + 18.5 = 13.425721582 Reorder the terms: 18.5 + x = 13.425721582 Solving 18.5 + x = 13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + x = 13.425721582 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = 13.425721582 + -18.5 x = 13.425721582 + -18.5 Combine like terms: 13.425721582 + -18.5 = -5.074278418 x = -5.074278418 Simplifying x = -5.074278418Subproblem 2
x + 18.5 = -13.425721582 Simplifying x + 18.5 = -13.425721582 Reorder the terms: 18.5 + x = -13.425721582 Solving 18.5 + x = -13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + x = -13.425721582 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = -13.425721582 + -18.5 x = -13.425721582 + -18.5 Combine like terms: -13.425721582 + -18.5 = -31.925721582 x = -31.925721582 Simplifying x = -31.925721582Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.074278418, -31.925721582}
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