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Simplifying 20x2 + -25x = -3 Reorder the terms: -25x + 20x2 = -3 Solving -25x + 20x2 = -3 Solving for variable 'x'. Reorder the terms: 3 + -25x + 20x2 = -3 + 3 Combine like terms: -3 + 3 = 0 3 + -25x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.15 + -1.25x + x2 = 0 Move the constant term to the right: Add '-0.15' to each side of the equation. 0.15 + -1.25x + -0.15 + x2 = 0 + -0.15 Reorder the terms: 0.15 + -0.15 + -1.25x + x2 = 0 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + -1.25x + x2 = 0 + -0.15 -1.25x + x2 = 0 + -0.15 Combine like terms: 0 + -0.15 = -0.15 -1.25x + x2 = -0.15 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = -0.15 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = -0.15 + 0.390625 Combine like terms: -0.15 + 0.390625 = 0.240625 0.390625 + -1.25x + x2 = 0.240625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 0.240625 Calculate the square root of the right side: 0.490535422 Break this problem into two subproblems by setting (x + -0.625) equal to 0.490535422 and -0.490535422.Subproblem 1
x + -0.625 = 0.490535422 Simplifying x + -0.625 = 0.490535422 Reorder the terms: -0.625 + x = 0.490535422 Solving -0.625 + x = 0.490535422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 0.490535422 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 0.490535422 + 0.625 x = 0.490535422 + 0.625 Combine like terms: 0.490535422 + 0.625 = 1.115535422 x = 1.115535422 Simplifying x = 1.115535422Subproblem 2
x + -0.625 = -0.490535422 Simplifying x + -0.625 = -0.490535422 Reorder the terms: -0.625 + x = -0.490535422 Solving -0.625 + x = -0.490535422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -0.490535422 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -0.490535422 + 0.625 x = -0.490535422 + 0.625 Combine like terms: -0.490535422 + 0.625 = 0.134464578 x = 0.134464578 Simplifying x = 0.134464578Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.115535422, 0.134464578}
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