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Simplifying 4x2 + -25x + 13 = -5 + 4 Reorder the terms: 13 + -25x + 4x2 = -5 + 4 Combine like terms: -5 + 4 = -1 13 + -25x + 4x2 = -1 Solving 13 + -25x + 4x2 = -1 Solving for variable 'x'. Reorder the terms: 13 + 1 + -25x + 4x2 = -1 + 1 Combine like terms: 13 + 1 = 14 14 + -25x + 4x2 = -1 + 1 Combine like terms: -1 + 1 = 0 14 + -25x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.5 + -6.25x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -6.25x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -6.25x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -6.25x + x2 = 0 + -3.5 -6.25x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -6.25x + x2 = -3.5 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = -3.5 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = -3.5 + 9.765625 Combine like terms: -3.5 + 9.765625 = 6.265625 9.765625 + -6.25x + x2 = 6.265625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 6.265625 Calculate the square root of the right side: 2.503123049 Break this problem into two subproblems by setting (x + -3.125) equal to 2.503123049 and -2.503123049.Subproblem 1
x + -3.125 = 2.503123049 Simplifying x + -3.125 = 2.503123049 Reorder the terms: -3.125 + x = 2.503123049 Solving -3.125 + x = 2.503123049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 2.503123049 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 2.503123049 + 3.125 x = 2.503123049 + 3.125 Combine like terms: 2.503123049 + 3.125 = 5.628123049 x = 5.628123049 Simplifying x = 5.628123049Subproblem 2
x + -3.125 = -2.503123049 Simplifying x + -3.125 = -2.503123049 Reorder the terms: -3.125 + x = -2.503123049 Solving -3.125 + x = -2.503123049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -2.503123049 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -2.503123049 + 3.125 x = -2.503123049 + 3.125 Combine like terms: -2.503123049 + 3.125 = 0.621876951 x = 0.621876951 Simplifying x = 0.621876951Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.628123049, 0.621876951}
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