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Simplifying (0.2 + -1x)(0.3 + -1x) = 0.25x2 Multiply (0.2 + -1x) * (0.3 + -1x) (0.2(0.3 + -1x) + -1x * (0.3 + -1x)) = 0.25x2 ((0.3 * 0.2 + -1x * 0.2) + -1x * (0.3 + -1x)) = 0.25x2 ((0.06 + -0.2x) + -1x * (0.3 + -1x)) = 0.25x2 (0.06 + -0.2x + (0.3 * -1x + -1x * -1x)) = 0.25x2 (0.06 + -0.2x + (-0.3x + 1x2)) = 0.25x2 Combine like terms: -0.2x + -0.3x = -0.5x (0.06 + -0.5x + 1x2) = 0.25x2 Solving 0.06 + -0.5x + 1x2 = 0.25x2 Solving for variable 'x'. Combine like terms: 1x2 + -0.25x2 = 0.75x2 0.06 + -0.5x + 0.75x2 = 0.25x2 + -0.25x2 Combine like terms: 0.25x2 + -0.25x2 = 0.00 0.06 + -0.5x + 0.75x2 = 0.00 Begin completing the square. Divide all terms by 0.75 the coefficient of the squared term: Divide each side by '0.75'. 0.08 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '-0.08' to each side of the equation. 0.08 + -0.6666666667x + -0.08 + x2 = 0 + -0.08 Reorder the terms: 0.08 + -0.08 + -0.6666666667x + x2 = 0 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + -0.6666666667x + x2 = 0 + -0.08 -0.6666666667x + x2 = 0 + -0.08 Combine like terms: 0 + -0.08 = -0.08 -0.6666666667x + x2 = -0.08 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = -0.08 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = -0.08 + 0.1111111112 Combine like terms: -0.08 + 0.1111111112 = 0.0311111112 0.1111111112 + -0.6666666667x + x2 = 0.0311111112 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 0.0311111112 Calculate the square root of the right side: 0.176383421 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 0.176383421 and -0.176383421.Subproblem 1
x + -0.3333333334 = 0.176383421 Simplifying x + -0.3333333334 = 0.176383421 Reorder the terms: -0.3333333334 + x = 0.176383421 Solving -0.3333333334 + x = 0.176383421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 0.176383421 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 0.176383421 + 0.3333333334 x = 0.176383421 + 0.3333333334 Combine like terms: 0.176383421 + 0.3333333334 = 0.5097167544 x = 0.5097167544 Simplifying x = 0.5097167544Subproblem 2
x + -0.3333333334 = -0.176383421 Simplifying x + -0.3333333334 = -0.176383421 Reorder the terms: -0.3333333334 + x = -0.176383421 Solving -0.3333333334 + x = -0.176383421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -0.176383421 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -0.176383421 + 0.3333333334 x = -0.176383421 + 0.3333333334 Combine like terms: -0.176383421 + 0.3333333334 = 0.1569499124 x = 0.1569499124 Simplifying x = 0.1569499124Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5097167544, 0.1569499124}
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