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Simplifying 2x2 + 15x + -56 = 0 Reorder the terms: -56 + 15x + 2x2 = 0 Solving -56 + 15x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -28 + 7.5x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + 7.5x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 7.5x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 7.5x + x2 = 0 + 28 7.5x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 7.5x + x2 = 28 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 28 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 28 + 14.0625 Combine like terms: 28 + 14.0625 = 42.0625 14.0625 + 7.5x + x2 = 42.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 42.0625 Calculate the square root of the right side: 6.485560886 Break this problem into two subproblems by setting (x + 3.75) equal to 6.485560886 and -6.485560886.Subproblem 1
x + 3.75 = 6.485560886 Simplifying x + 3.75 = 6.485560886 Reorder the terms: 3.75 + x = 6.485560886 Solving 3.75 + x = 6.485560886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 6.485560886 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 6.485560886 + -3.75 x = 6.485560886 + -3.75 Combine like terms: 6.485560886 + -3.75 = 2.735560886 x = 2.735560886 Simplifying x = 2.735560886Subproblem 2
x + 3.75 = -6.485560886 Simplifying x + 3.75 = -6.485560886 Reorder the terms: 3.75 + x = -6.485560886 Solving 3.75 + x = -6.485560886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -6.485560886 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -6.485560886 + -3.75 x = -6.485560886 + -3.75 Combine like terms: -6.485560886 + -3.75 = -10.235560886 x = -10.235560886 Simplifying x = -10.235560886Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.735560886, -10.235560886}
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