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Simplifying 2 + -2x + -1x + x * x = 0.04x * x Multiply x * x 2 + -2x + -1x + x2 = 0.04x * x Combine like terms: -2x + -1x = -3x 2 + -3x + x2 = 0.04x * x Multiply x * x 2 + -3x + x2 = 0.04x2 Solving 2 + -3x + x2 = 0.04x2 Solving for variable 'x'. Combine like terms: x2 + -0.04x2 = 0.96x2 2 + -3x + 0.96x2 = 0.04x2 + -0.04x2 Combine like terms: 0.04x2 + -0.04x2 = 0.00 2 + -3x + 0.96x2 = 0.00 Begin completing the square. Divide all terms by 0.96 the coefficient of the squared term: Divide each side by '0.96'. 2.083333333 + -3.125x + x2 = 0 Move the constant term to the right: Add '-2.083333333' to each side of the equation. 2.083333333 + -3.125x + -2.083333333 + x2 = 0 + -2.083333333 Reorder the terms: 2.083333333 + -2.083333333 + -3.125x + x2 = 0 + -2.083333333 Combine like terms: 2.083333333 + -2.083333333 = 0.000000000 0.000000000 + -3.125x + x2 = 0 + -2.083333333 -3.125x + x2 = 0 + -2.083333333 Combine like terms: 0 + -2.083333333 = -2.083333333 -3.125x + x2 = -2.083333333 The x term is -3.125x. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125x + 2.44140625 + x2 = -2.083333333 + 2.44140625 Reorder the terms: 2.44140625 + -3.125x + x2 = -2.083333333 + 2.44140625 Combine like terms: -2.083333333 + 2.44140625 = 0.358072917 2.44140625 + -3.125x + x2 = 0.358072917 Factor a perfect square on the left side: (x + -1.5625)(x + -1.5625) = 0.358072917 Calculate the square root of the right side: 0.598391943 Break this problem into two subproblems by setting (x + -1.5625) equal to 0.598391943 and -0.598391943.Subproblem 1
x + -1.5625 = 0.598391943 Simplifying x + -1.5625 = 0.598391943 Reorder the terms: -1.5625 + x = 0.598391943 Solving -1.5625 + x = 0.598391943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = 0.598391943 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = 0.598391943 + 1.5625 x = 0.598391943 + 1.5625 Combine like terms: 0.598391943 + 1.5625 = 2.160891943 x = 2.160891943 Simplifying x = 2.160891943Subproblem 2
x + -1.5625 = -0.598391943 Simplifying x + -1.5625 = -0.598391943 Reorder the terms: -1.5625 + x = -0.598391943 Solving -1.5625 + x = -0.598391943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = -0.598391943 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = -0.598391943 + 1.5625 x = -0.598391943 + 1.5625 Combine like terms: -0.598391943 + 1.5625 = 0.964108057 x = 0.964108057 Simplifying x = 0.964108057Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.160891943, 0.964108057}
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