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Simplifying 8x2 + -37x + -25 = -2 Reorder the terms: -25 + -37x + 8x2 = -2 Solving -25 + -37x + 8x2 = -2 Solving for variable 'x'. Reorder the terms: -25 + 2 + -37x + 8x2 = -2 + 2 Combine like terms: -25 + 2 = -23 -23 + -37x + 8x2 = -2 + 2 Combine like terms: -2 + 2 = 0 -23 + -37x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.875 + -4.625x + x2 = 0 Move the constant term to the right: Add '2.875' to each side of the equation. -2.875 + -4.625x + 2.875 + x2 = 0 + 2.875 Reorder the terms: -2.875 + 2.875 + -4.625x + x2 = 0 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + -4.625x + x2 = 0 + 2.875 -4.625x + x2 = 0 + 2.875 Combine like terms: 0 + 2.875 = 2.875 -4.625x + x2 = 2.875 The x term is -4.625x. Take half its coefficient (-2.3125). Square it (5.34765625) and add it to both sides. Add '5.34765625' to each side of the equation. -4.625x + 5.34765625 + x2 = 2.875 + 5.34765625 Reorder the terms: 5.34765625 + -4.625x + x2 = 2.875 + 5.34765625 Combine like terms: 2.875 + 5.34765625 = 8.22265625 5.34765625 + -4.625x + x2 = 8.22265625 Factor a perfect square on the left side: (x + -2.3125)(x + -2.3125) = 8.22265625 Calculate the square root of the right side: 2.867517437 Break this problem into two subproblems by setting (x + -2.3125) equal to 2.867517437 and -2.867517437.Subproblem 1
x + -2.3125 = 2.867517437 Simplifying x + -2.3125 = 2.867517437 Reorder the terms: -2.3125 + x = 2.867517437 Solving -2.3125 + x = 2.867517437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3125' to each side of the equation. -2.3125 + 2.3125 + x = 2.867517437 + 2.3125 Combine like terms: -2.3125 + 2.3125 = 0.0000 0.0000 + x = 2.867517437 + 2.3125 x = 2.867517437 + 2.3125 Combine like terms: 2.867517437 + 2.3125 = 5.180017437 x = 5.180017437 Simplifying x = 5.180017437Subproblem 2
x + -2.3125 = -2.867517437 Simplifying x + -2.3125 = -2.867517437 Reorder the terms: -2.3125 + x = -2.867517437 Solving -2.3125 + x = -2.867517437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3125' to each side of the equation. -2.3125 + 2.3125 + x = -2.867517437 + 2.3125 Combine like terms: -2.3125 + 2.3125 = 0.0000 0.0000 + x = -2.867517437 + 2.3125 x = -2.867517437 + 2.3125 Combine like terms: -2.867517437 + 2.3125 = -0.555017437 x = -0.555017437 Simplifying x = -0.555017437Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.180017437, -0.555017437}
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