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Simplifying 8x2 + 24x = -15 Reorder the terms: 24x + 8x2 = -15 Solving 24x + 8x2 = -15 Solving for variable 'x'. Reorder the terms: 15 + 24x + 8x2 = -15 + 15 Combine like terms: -15 + 15 = 0 15 + 24x + 8x2 = 0 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 = 0.375 2.25 + 3x + x2 = 0.375 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 0.375 Calculate the square root of the right side: 0.612372436 Break this problem into two subproblems by setting (x + 1.5) equal to 0.612372436 and -0.612372436.Subproblem 1
x + 1.5 = 0.612372436 Simplifying x + 1.5 = 0.612372436 Reorder the terms: 1.5 + x = 0.612372436 Solving 1.5 + x = 0.612372436 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 = 0.612372436 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 0.612372436 + -1.5 x = 0.612372436 + -1.5 Combine like terms: 0.612372436 + -1.5 = -0.887627564 x = -0.887627564 Simplifying x = -0.887627564Subproblem 2
x + 1.5 = -0.612372436 Simplifying x + 1.5 = -0.612372436 Reorder the terms: 1.5 + x = -0.612372436 Solving 1.5 + x = -0.612372436 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 = -0.612372436 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -0.612372436 + -1.5 x = -0.612372436 + -1.5 Combine like terms: -0.612372436 + -1.5 = -2.112372436 x = -2.112372436 Simplifying x = -2.112372436Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.887627564, -2.112372436}
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