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Simplifying x2 + 15x + -1296 = 0 Reorder the terms: -1296 + 15x + x2 = 0 Solving -1296 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1296' to each side of the equation. -1296 + 15x + 1296 + x2 = 0 + 1296 Reorder the terms: -1296 + 1296 + 15x + x2 = 0 + 1296 Combine like terms: -1296 + 1296 = 0 0 + 15x + x2 = 0 + 1296 15x + x2 = 0 + 1296 Combine like terms: 0 + 1296 = 1296 15x + x2 = 1296 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 = 1296 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 1296 + 56.25 Combine like terms: 1296 + 56.25 = 1352.25 56.25 + 15x + x2 = 1352.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 1352.25 Calculate the square root of the right side: 36.772952016 Break this problem into two subproblems by setting (x + 7.5) equal to 36.772952016 and -36.772952016.Subproblem 1
x + 7.5 = 36.772952016 Simplifying x + 7.5 = 36.772952016 Reorder the terms: 7.5 + x = 36.772952016 Solving 7.5 + x = 36.772952016 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 = 36.772952016 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 36.772952016 + -7.5 x = 36.772952016 + -7.5 Combine like terms: 36.772952016 + -7.5 = 29.272952016 x = 29.272952016 Simplifying x = 29.272952016Subproblem 2
x + 7.5 = -36.772952016 Simplifying x + 7.5 = -36.772952016 Reorder the terms: 7.5 + x = -36.772952016 Solving 7.5 + x = -36.772952016 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 = -36.772952016 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -36.772952016 + -7.5 x = -36.772952016 + -7.5 Combine like terms: -36.772952016 + -7.5 = -44.272952016 x = -44.272952016 Simplifying x = -44.272952016Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.272952016, -44.272952016}
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