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Simplifying (2.0 + -1x)(0.8 + -1x) = 0 Multiply (2.0 + -1x) * (0.8 + -1x) (2.0(0.8 + -1x) + -1x * (0.8 + -1x)) = 0 ((0.8 * 2.0 + -1x * 2.0) + -1x * (0.8 + -1x)) = 0 ((1.6 + -2x) + -1x * (0.8 + -1x)) = 0 (1.6 + -2x + (0.8 * -1x + -1x * -1x)) = 0 (1.6 + -2x + (-0.8x + 1x2)) = 0 Combine like terms: -2x + -0.8x = -2.8x (1.6 + -2.8x + 1x2) = 0 Solving 1.6 + -2.8x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + -2.8x + -1.6 + x2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + -2.8x + x2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + -2.8x + x2 = 0 + -1.6 -2.8x + x2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 -2.8x + x2 = -1.6 The x term is -2.8x. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8x + 1.96 + x2 = -1.6 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = -1.6 + 1.96 Combine like terms: -1.6 + 1.96 = 0.36 1.96 + -2.8x + x2 = 0.36 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = 0.36 Calculate the square root of the right side: 0.6 Break this problem into two subproblems by setting (x + -1.4) equal to 0.6 and -0.6.Subproblem 1
x + -1.4 = 0.6 Simplifying x + -1.4 = 0.6 Reorder the terms: -1.4 + x = 0.6 Solving -1.4 + x = 0.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = 0.6 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 0.6 + 1.4 x = 0.6 + 1.4 Combine like terms: 0.6 + 1.4 = 2 x = 2 Simplifying x = 2Subproblem 2
x + -1.4 = -0.6 Simplifying x + -1.4 = -0.6 Reorder the terms: -1.4 + x = -0.6 Solving -1.4 + x = -0.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = -0.6 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -0.6 + 1.4 x = -0.6 + 1.4 Combine like terms: -0.6 + 1.4 = 0.8 x = 0.8 Simplifying x = 0.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, 0.8}
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