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Simplifying (0.1 + -1x)(1.5 + -1x) = 0 Multiply (0.1 + -1x) * (1.5 + -1x) (0.1(1.5 + -1x) + -1x * (1.5 + -1x)) = 0 ((1.5 * 0.1 + -1x * 0.1) + -1x * (1.5 + -1x)) = 0 ((0.15 + -0.1x) + -1x * (1.5 + -1x)) = 0 (0.15 + -0.1x + (1.5 * -1x + -1x * -1x)) = 0 (0.15 + -0.1x + (-1.5x + 1x2)) = 0 Combine like terms: -0.1x + -1.5x = -1.6x (0.15 + -1.6x + 1x2) = 0 Solving 0.15 + -1.6x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.15' to each side of the equation. 0.15 + -1.6x + -0.15 + x2 = 0 + -0.15 Reorder the terms: 0.15 + -0.15 + -1.6x + x2 = 0 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + -1.6x + x2 = 0 + -0.15 -1.6x + x2 = 0 + -0.15 Combine like terms: 0 + -0.15 = -0.15 -1.6x + x2 = -0.15 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = -0.15 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = -0.15 + 0.64 Combine like terms: -0.15 + 0.64 = 0.49 0.64 + -1.6x + x2 = 0.49 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 0.49 Calculate the square root of the right side: 0.7 Break this problem into two subproblems by setting (x + -0.8) equal to 0.7 and -0.7.Subproblem 1
x + -0.8 = 0.7 Simplifying x + -0.8 = 0.7 Reorder the terms: -0.8 + x = 0.7 Solving -0.8 + x = 0.7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 0.7 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 0.7 + 0.8 x = 0.7 + 0.8 Combine like terms: 0.7 + 0.8 = 1.5 x = 1.5 Simplifying x = 1.5Subproblem 2
x + -0.8 = -0.7 Simplifying x + -0.8 = -0.7 Reorder the terms: -0.8 + x = -0.7 Solving -0.8 + x = -0.7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -0.7 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -0.7 + 0.8 x = -0.7 + 0.8 Combine like terms: -0.7 + 0.8 = 0.1 x = 0.1 Simplifying x = 0.1Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5, 0.1}
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