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Simplifying x2 + 15x = 124 Reorder the terms: 15x + x2 = 124 Solving 15x + x2 = 124 Solving for variable 'x'. Reorder the terms: -124 + 15x + x2 = 124 + -124 Combine like terms: 124 + -124 = 0 -124 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '124' to each side of the equation. -124 + 15x + 124 + x2 = 0 + 124 Reorder the terms: -124 + 124 + 15x + x2 = 0 + 124 Combine like terms: -124 + 124 = 0 0 + 15x + x2 = 0 + 124 15x + x2 = 0 + 124 Combine like terms: 0 + 124 = 124 15x + x2 = 124 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 124 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 124 + 56.25 Combine like terms: 124 + 56.25 = 180.25 56.25 + 15x + x2 = 180.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 180.25 Calculate the square root of the right side: 13.425721582 Break this problem into two subproblems by setting (x + 7.5) equal to 13.425721582 and -13.425721582.Subproblem 1
x + 7.5 = 13.425721582 Simplifying x + 7.5 = 13.425721582 Reorder the terms: 7.5 + x = 13.425721582 Solving 7.5 + x = 13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 13.425721582 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 13.425721582 + -7.5 x = 13.425721582 + -7.5 Combine like terms: 13.425721582 + -7.5 = 5.925721582 x = 5.925721582 Simplifying x = 5.925721582Subproblem 2
x + 7.5 = -13.425721582 Simplifying x + 7.5 = -13.425721582 Reorder the terms: 7.5 + x = -13.425721582 Solving 7.5 + x = -13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -13.425721582 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -13.425721582 + -7.5 x = -13.425721582 + -7.5 Combine like terms: -13.425721582 + -7.5 = -20.925721582 x = -20.925721582 Simplifying x = -20.925721582Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.925721582, -20.925721582}
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