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Simplifying 8x2 + 24x + -25 = 0 Reorder the terms: -25 + 24x + 8x2 = 0 Solving -25 + 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'. -3.125 + 3x + x2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + 3x + 3.125 + x2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + 3x + x2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + 3x + x2 = 0 + 3.125 3x + x2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 3x + x2 = 3.125 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 = 3.125 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 3.125 + 2.25 Combine like terms: 3.125 + 2.25 = 5.375 2.25 + 3x + x2 = 5.375 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 5.375 Calculate the square root of the right side: 2.318404624 Break this problem into two subproblems by setting (x + 1.5) equal to 2.318404624 and -2.318404624.Subproblem 1
x + 1.5 = 2.318404624 Simplifying x + 1.5 = 2.318404624 Reorder the terms: 1.5 + x = 2.318404624 Solving 1.5 + x = 2.318404624 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 = 2.318404624 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.318404624 + -1.5 x = 2.318404624 + -1.5 Combine like terms: 2.318404624 + -1.5 = 0.818404624 x = 0.818404624 Simplifying x = 0.818404624Subproblem 2
x + 1.5 = -2.318404624 Simplifying x + 1.5 = -2.318404624 Reorder the terms: 1.5 + x = -2.318404624 Solving 1.5 + x = -2.318404624 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 = -2.318404624 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.318404624 + -1.5 x = -2.318404624 + -1.5 Combine like terms: -2.318404624 + -1.5 = -3.818404624 x = -3.818404624 Simplifying x = -3.818404624Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.818404624, -3.818404624}
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