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Simplifying 4x2 + -25x + 23 = -5 + 2 Reorder the terms: 23 + -25x + 4x2 = -5 + 2 Combine like terms: -5 + 2 = -3 23 + -25x + 4x2 = -3 Solving 23 + -25x + 4x2 = -3 Solving for variable 'x'. Reorder the terms: 23 + 3 + -25x + 4x2 = -3 + 3 Combine like terms: 23 + 3 = 26 26 + -25x + 4x2 = -3 + 3 Combine like terms: -3 + 3 = 0 26 + -25x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.5 + -6.25x + x2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -6.25x + -6.5 + x2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -6.25x + x2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -6.25x + x2 = 0 + -6.5 -6.25x + x2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -6.25x + x2 = -6.5 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 = -6.5 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = -6.5 + 9.765625 Combine like terms: -6.5 + 9.765625 = 3.265625 9.765625 + -6.25x + x2 = 3.265625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 3.265625 Calculate the square root of the right side: 1.807104037 Break this problem into two subproblems by setting (x + -3.125) equal to 1.807104037 and -1.807104037.Subproblem 1
x + -3.125 = 1.807104037 Simplifying x + -3.125 = 1.807104037 Reorder the terms: -3.125 + x = 1.807104037 Solving -3.125 + x = 1.807104037 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 = 1.807104037 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 1.807104037 + 3.125 x = 1.807104037 + 3.125 Combine like terms: 1.807104037 + 3.125 = 4.932104037 x = 4.932104037 Simplifying x = 4.932104037Subproblem 2
x + -3.125 = -1.807104037 Simplifying x + -3.125 = -1.807104037 Reorder the terms: -3.125 + x = -1.807104037 Solving -3.125 + x = -1.807104037 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 = -1.807104037 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -1.807104037 + 3.125 x = -1.807104037 + 3.125 Combine like terms: -1.807104037 + 3.125 = 1.317895963 x = 1.317895963 Simplifying x = 1.317895963Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.932104037, 1.317895963}
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