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Simplifying ((0.30 + -1x)(0.40 + -1x)) = 0 Multiply (0.30 + -1x) * (0.40 + -1x) ((0.30(0.40 + -1x) + -1x * (0.40 + -1x))) = 0 (((0.40 * 0.30 + -1x * 0.30) + -1x * (0.40 + -1x))) = 0 (((0.12 + -0.3x) + -1x * (0.40 + -1x))) = 0 ((0.12 + -0.3x + (0.40 * -1x + -1x * -1x))) = 0 ((0.12 + -0.3x + (-0.4x + 1x2))) = 0 Combine like terms: -0.3x + -0.4x = -0.7x ((0.12 + -0.7x + 1x2)) = 0 (0.12 + -0.7x + 1x2) = 0 Remove parenthesis around (0.12 + -0.7x + 1x2) 0.12 + -0.7x + 1x2 = 0 Solving 0.12 + -0.7x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.12' to each side of the equation. 0.12 + -0.7x + -0.12 + x2 = 0 + -0.12 Reorder the terms: 0.12 + -0.12 + -0.7x + x2 = 0 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + -0.7x + x2 = 0 + -0.12 -0.7x + x2 = 0 + -0.12 Combine like terms: 0 + -0.12 = -0.12 -0.7x + x2 = -0.12 The x term is -0.7x. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7x + 0.1225 + x2 = -0.12 + 0.1225 Reorder the terms: 0.1225 + -0.7x + x2 = -0.12 + 0.1225 Combine like terms: -0.12 + 0.1225 = 0.0025 0.1225 + -0.7x + x2 = 0.0025 Factor a perfect square on the left side: (x + -0.35)(x + -0.35) = 0.0025 Calculate the square root of the right side: 0.05 Break this problem into two subproblems by setting (x + -0.35) equal to 0.05 and -0.05.Subproblem 1
x + -0.35 = 0.05 Simplifying x + -0.35 = 0.05 Reorder the terms: -0.35 + x = 0.05 Solving -0.35 + x = 0.05 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = 0.05 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = 0.05 + 0.35 x = 0.05 + 0.35 Combine like terms: 0.05 + 0.35 = 0.4 x = 0.4 Simplifying x = 0.4Subproblem 2
x + -0.35 = -0.05 Simplifying x + -0.35 = -0.05 Reorder the terms: -0.35 + x = -0.05 Solving -0.35 + x = -0.05 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = -0.05 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = -0.05 + 0.35 x = -0.05 + 0.35 Combine like terms: -0.05 + 0.35 = 0.3 x = 0.3 Simplifying x = 0.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4, 0.3}
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