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Simplifying 8x2 + 24x + -15 = 0 Reorder the terms: -15 + 24x + 8x2 = 0 Solving -15 + 24x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.875 + 3x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + 3x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + 3x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + 3x + x2 = 0 + 1.875 3x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 3x + x2 = 1.875 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 1.875 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 1.875 + 2.25 Combine like terms: 1.875 + 2.25 = 4.125 2.25 + 3x + x2 = 4.125 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 4.125 Calculate the square root of the right side: 2.031009601 Break this problem into two subproblems by setting (x + 1.5) equal to 2.031009601 and -2.031009601.Subproblem 1
x + 1.5 = 2.031009601 Simplifying x + 1.5 = 2.031009601 Reorder the terms: 1.5 + x = 2.031009601 Solving 1.5 + x = 2.031009601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.031009601 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.031009601 + -1.5 x = 2.031009601 + -1.5 Combine like terms: 2.031009601 + -1.5 = 0.531009601 x = 0.531009601 Simplifying x = 0.531009601Subproblem 2
x + 1.5 = -2.031009601 Simplifying x + 1.5 = -2.031009601 Reorder the terms: 1.5 + x = -2.031009601 Solving 1.5 + x = -2.031009601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.031009601 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.031009601 + -1.5 x = -2.031009601 + -1.5 Combine like terms: -2.031009601 + -1.5 = -3.531009601 x = -3.531009601 Simplifying x = -3.531009601Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.531009601, -3.531009601}
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