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Simplifying 4x2 + -25x + 12 = 0 Reorder the terms: 12 + -25x + 4x2 = 0 Solving 12 + -25x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3 + -6.25x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -6.25x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -6.25x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -6.25x + x2 = 0 + -3 -6.25x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -6.25x + x2 = -3 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 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = -3 + 9.765625 Combine like terms: -3 + 9.765625 = 6.765625 9.765625 + -6.25x + x2 = 6.765625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 6.765625 Calculate the square root of the right side: 2.601081506 Break this problem into two subproblems by setting (x + -3.125) equal to 2.601081506 and -2.601081506.Subproblem 1
x + -3.125 = 2.601081506 Simplifying x + -3.125 = 2.601081506 Reorder the terms: -3.125 + x = 2.601081506 Solving -3.125 + x = 2.601081506 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 = 2.601081506 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 2.601081506 + 3.125 x = 2.601081506 + 3.125 Combine like terms: 2.601081506 + 3.125 = 5.726081506 x = 5.726081506 Simplifying x = 5.726081506Subproblem 2
x + -3.125 = -2.601081506 Simplifying x + -3.125 = -2.601081506 Reorder the terms: -3.125 + x = -2.601081506 Solving -3.125 + x = -2.601081506 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 = -2.601081506 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -2.601081506 + 3.125 x = -2.601081506 + 3.125 Combine like terms: -2.601081506 + 3.125 = 0.523918494 x = 0.523918494 Simplifying x = 0.523918494Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.726081506, 0.523918494}
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