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Simplifying (2x + -3)(5x + -1) = 2x + 0.4 Reorder the terms: (-3 + 2x)(5x + -1) = 2x + 0.4 Reorder the terms: (-3 + 2x)(-1 + 5x) = 2x + 0.4 Multiply (-3 + 2x) * (-1 + 5x) (-3(-1 + 5x) + 2x * (-1 + 5x)) = 2x + 0.4 ((-1 * -3 + 5x * -3) + 2x * (-1 + 5x)) = 2x + 0.4 ((3 + -15x) + 2x * (-1 + 5x)) = 2x + 0.4 (3 + -15x + (-1 * 2x + 5x * 2x)) = 2x + 0.4 (3 + -15x + (-2x + 10x2)) = 2x + 0.4 Combine like terms: -15x + -2x = -17x (3 + -17x + 10x2) = 2x + 0.4 Reorder the terms: 3 + -17x + 10x2 = 0.4 + 2x Solving 3 + -17x + 10x2 = 0.4 + 2x Solving for variable 'x'. Reorder the terms: 3 + -0.4 + -17x + -2x + 10x2 = 0.4 + 2x + -0.4 + -2x Combine like terms: 3 + -0.4 = 2.6 2.6 + -17x + -2x + 10x2 = 0.4 + 2x + -0.4 + -2x Combine like terms: -17x + -2x = -19x 2.6 + -19x + 10x2 = 0.4 + 2x + -0.4 + -2x Reorder the terms: 2.6 + -19x + 10x2 = 0.4 + -0.4 + 2x + -2x Combine like terms: 0.4 + -0.4 = 0.0 2.6 + -19x + 10x2 = 0.0 + 2x + -2x 2.6 + -19x + 10x2 = 2x + -2x Combine like terms: 2x + -2x = 0 2.6 + -19x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.26 + -1.9x + x2 = 0.0 Move the constant term to the right: Add '-0.26' to each side of the equation. 0.26 + -1.9x + -0.26 + x2 = 0.0 + -0.26 Reorder the terms: 0.26 + -0.26 + -1.9x + x2 = 0.0 + -0.26 Combine like terms: 0.26 + -0.26 = 0.00 0.00 + -1.9x + x2 = 0.0 + -0.26 -1.9x + x2 = 0.0 + -0.26 Combine like terms: 0.0 + -0.26 = -0.26 -1.9x + x2 = -0.26 The x term is -1.9x. Take half its coefficient (-0.95). Square it (0.9025) and add it to both sides. Add '0.9025' to each side of the equation. -1.9x + 0.9025 + x2 = -0.26 + 0.9025 Reorder the terms: 0.9025 + -1.9x + x2 = -0.26 + 0.9025 Combine like terms: -0.26 + 0.9025 = 0.6425 0.9025 + -1.9x + x2 = 0.6425 Factor a perfect square on the left side: (x + -0.95)(x + -0.95) = 0.6425 Calculate the square root of the right side: 0.801560977 Break this problem into two subproblems by setting (x + -0.95) equal to 0.801560977 and -0.801560977.Subproblem 1
x + -0.95 = 0.801560977 Simplifying x + -0.95 = 0.801560977 Reorder the terms: -0.95 + x = 0.801560977 Solving -0.95 + x = 0.801560977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + x = 0.801560977 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + x = 0.801560977 + 0.95 x = 0.801560977 + 0.95 Combine like terms: 0.801560977 + 0.95 = 1.751560977 x = 1.751560977 Simplifying x = 1.751560977Subproblem 2
x + -0.95 = -0.801560977 Simplifying x + -0.95 = -0.801560977 Reorder the terms: -0.95 + x = -0.801560977 Solving -0.95 + x = -0.801560977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + x = -0.801560977 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + x = -0.801560977 + 0.95 x = -0.801560977 + 0.95 Combine like terms: -0.801560977 + 0.95 = 0.148439023 x = 0.148439023 Simplifying x = 0.148439023Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.751560977, 0.148439023}
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