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Simplifying x + -1(0.24 + x)(0.20 + x) = 0 Multiply (0.24 + x) * (0.20 + x) x + -1(0.24(0.20 + x) + x(0.20 + x)) = 0 x + -1((0.20 * 0.24 + x * 0.24) + x(0.20 + x)) = 0 x + -1((0.048 + 0.24x) + x(0.20 + x)) = 0 x + -1(0.048 + 0.24x + (0.20 * x + x * x)) = 0 x + -1(0.048 + 0.24x + (0.20x + x2)) = 0 Combine like terms: 0.24x + 0.20x = 0.44x x + -1(0.048 + 0.44x + x2) = 0 x + (0.048 * -1 + 0.44x * -1 + x2 * -1) = 0 x + (-0.048 + -0.44x + -1x2) = 0 Reorder the terms: -0.048 + x + -0.44x + -1x2 = 0 Combine like terms: x + -0.44x = 0.56x -0.048 + 0.56x + -1x2 = 0 Solving -0.048 + 0.56x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.048 + -0.56x + x2 = 0 Move the constant term to the right: Add '-0.048' to each side of the equation. 0.048 + -0.56x + -0.048 + x2 = 0 + -0.048 Reorder the terms: 0.048 + -0.048 + -0.56x + x2 = 0 + -0.048 Combine like terms: 0.048 + -0.048 = 0.000 0.000 + -0.56x + x2 = 0 + -0.048 -0.56x + x2 = 0 + -0.048 Combine like terms: 0 + -0.048 = -0.048 -0.56x + x2 = -0.048 The x term is -0.56x. Take half its coefficient (-0.28). Square it (0.0784) and add it to both sides. Add '0.0784' to each side of the equation. -0.56x + 0.0784 + x2 = -0.048 + 0.0784 Reorder the terms: 0.0784 + -0.56x + x2 = -0.048 + 0.0784 Combine like terms: -0.048 + 0.0784 = 0.0304 0.0784 + -0.56x + x2 = 0.0304 Factor a perfect square on the left side: (x + -0.28)(x + -0.28) = 0.0304 Calculate the square root of the right side: 0.174355958 Break this problem into two subproblems by setting (x + -0.28) equal to 0.174355958 and -0.174355958.Subproblem 1
x + -0.28 = 0.174355958 Simplifying x + -0.28 = 0.174355958 Reorder the terms: -0.28 + x = 0.174355958 Solving -0.28 + x = 0.174355958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28' to each side of the equation. -0.28 + 0.28 + x = 0.174355958 + 0.28 Combine like terms: -0.28 + 0.28 = 0.00 0.00 + x = 0.174355958 + 0.28 x = 0.174355958 + 0.28 Combine like terms: 0.174355958 + 0.28 = 0.454355958 x = 0.454355958 Simplifying x = 0.454355958Subproblem 2
x + -0.28 = -0.174355958 Simplifying x + -0.28 = -0.174355958 Reorder the terms: -0.28 + x = -0.174355958 Solving -0.28 + x = -0.174355958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28' to each side of the equation. -0.28 + 0.28 + x = -0.174355958 + 0.28 Combine like terms: -0.28 + 0.28 = 0.00 0.00 + x = -0.174355958 + 0.28 x = -0.174355958 + 0.28 Combine like terms: -0.174355958 + 0.28 = 0.105644042 x = 0.105644042 Simplifying x = 0.105644042Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.454355958, 0.105644042}
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