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Simplifying x2 + 15x + -416 = 0 Reorder the terms: -416 + 15x + x2 = 0 Solving -416 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '416' to each side of the equation. -416 + 15x + 416 + x2 = 0 + 416 Reorder the terms: -416 + 416 + 15x + x2 = 0 + 416 Combine like terms: -416 + 416 = 0 0 + 15x + x2 = 0 + 416 15x + x2 = 0 + 416 Combine like terms: 0 + 416 = 416 15x + x2 = 416 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 = 416 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 416 + 56.25 Combine like terms: 416 + 56.25 = 472.25 56.25 + 15x + x2 = 472.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 472.25 Calculate the square root of the right side: 21.731313812 Break this problem into two subproblems by setting (x + 7.5) equal to 21.731313812 and -21.731313812.Subproblem 1
x + 7.5 = 21.731313812 Simplifying x + 7.5 = 21.731313812 Reorder the terms: 7.5 + x = 21.731313812 Solving 7.5 + x = 21.731313812 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 = 21.731313812 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 21.731313812 + -7.5 x = 21.731313812 + -7.5 Combine like terms: 21.731313812 + -7.5 = 14.231313812 x = 14.231313812 Simplifying x = 14.231313812Subproblem 2
x + 7.5 = -21.731313812 Simplifying x + 7.5 = -21.731313812 Reorder the terms: 7.5 + x = -21.731313812 Solving 7.5 + x = -21.731313812 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 = -21.731313812 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -21.731313812 + -7.5 x = -21.731313812 + -7.5 Combine like terms: -21.731313812 + -7.5 = -29.231313812 x = -29.231313812 Simplifying x = -29.231313812Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.231313812, -29.231313812}
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