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Simplifying (0.8 + -1x)(1.2 + -1x) = 0 Multiply (0.8 + -1x) * (1.2 + -1x) (0.8(1.2 + -1x) + -1x * (1.2 + -1x)) = 0 ((1.2 * 0.8 + -1x * 0.8) + -1x * (1.2 + -1x)) = 0 ((0.96 + -0.8x) + -1x * (1.2 + -1x)) = 0 (0.96 + -0.8x + (1.2 * -1x + -1x * -1x)) = 0 (0.96 + -0.8x + (-1.2x + 1x2)) = 0 Combine like terms: -0.8x + -1.2x = -2x (0.96 + -2x + 1x2) = 0 Solving 0.96 + -2x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.96' to each side of the equation. 0.96 + -2x + -0.96 + x2 = 0 + -0.96 Reorder the terms: 0.96 + -0.96 + -2x + x2 = 0 + -0.96 Combine like terms: 0.96 + -0.96 = 0.00 0.00 + -2x + x2 = 0 + -0.96 -2x + x2 = 0 + -0.96 Combine like terms: 0 + -0.96 = -0.96 -2x + x2 = -0.96 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.96 + 1 Reorder the terms: 1 + -2x + x2 = -0.96 + 1 Combine like terms: -0.96 + 1 = 0.04 1 + -2x + x2 = 0.04 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.04 Calculate the square root of the right side: 0.2 Break this problem into two subproblems by setting (x + -1) equal to 0.2 and -0.2.Subproblem 1
x + -1 = 0.2 Simplifying x + -1 = 0.2 Reorder the terms: -1 + x = 0.2 Solving -1 + x = 0.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.2 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.2 + 1 x = 0.2 + 1 Combine like terms: 0.2 + 1 = 1.2 x = 1.2 Simplifying x = 1.2Subproblem 2
x + -1 = -0.2 Simplifying x + -1 = -0.2 Reorder the terms: -1 + x = -0.2 Solving -1 + x = -0.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.2 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.2 + 1 x = -0.2 + 1 Combine like terms: -0.2 + 1 = 0.8 x = 0.8 Simplifying x = 0.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2, 0.8}
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