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Simplifying x2 + 15x + -376 = 0 Reorder the terms: -376 + 15x + x2 = 0 Solving -376 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '376' to each side of the equation. -376 + 15x + 376 + x2 = 0 + 376 Reorder the terms: -376 + 376 + 15x + x2 = 0 + 376 Combine like terms: -376 + 376 = 0 0 + 15x + x2 = 0 + 376 15x + x2 = 0 + 376 Combine like terms: 0 + 376 = 376 15x + x2 = 376 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 = 376 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 376 + 56.25 Combine like terms: 376 + 56.25 = 432.25 56.25 + 15x + x2 = 432.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 432.25 Calculate the square root of the right side: 20.790622886 Break this problem into two subproblems by setting (x + 7.5) equal to 20.790622886 and -20.790622886.Subproblem 1
x + 7.5 = 20.790622886 Simplifying x + 7.5 = 20.790622886 Reorder the terms: 7.5 + x = 20.790622886 Solving 7.5 + x = 20.790622886 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 = 20.790622886 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 20.790622886 + -7.5 x = 20.790622886 + -7.5 Combine like terms: 20.790622886 + -7.5 = 13.290622886 x = 13.290622886 Simplifying x = 13.290622886Subproblem 2
x + 7.5 = -20.790622886 Simplifying x + 7.5 = -20.790622886 Reorder the terms: 7.5 + x = -20.790622886 Solving 7.5 + x = -20.790622886 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 = -20.790622886 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -20.790622886 + -7.5 x = -20.790622886 + -7.5 Combine like terms: -20.790622886 + -7.5 = -28.290622886 x = -28.290622886 Simplifying x = -28.290622886Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.290622886, -28.290622886}
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