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Simplifying x2 + -0.1x = 0.12 Reorder the terms: -0.1x + x2 = 0.12 Solving -0.1x + x2 = 0.12 Solving for variable 'x'. Reorder the terms: -0.12 + -0.1x + x2 = 0.12 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 -0.12 + -0.1x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.12' to each side of the equation. -0.12 + -0.1x + 0.12 + x2 = 0.00 + 0.12 Reorder the terms: -0.12 + 0.12 + -0.1x + x2 = 0.00 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + -0.1x + x2 = 0.00 + 0.12 -0.1x + x2 = 0.00 + 0.12 Combine like terms: 0.00 + 0.12 = 0.12 -0.1x + x2 = 0.12 The x term is -0.1x. Take half its coefficient (-0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. -0.1x + 0.0025 + x2 = 0.12 + 0.0025 Reorder the terms: 0.0025 + -0.1x + x2 = 0.12 + 0.0025 Combine like terms: 0.12 + 0.0025 = 0.1225 0.0025 + -0.1x + x2 = 0.1225 Factor a perfect square on the left side: (x + -0.05)(x + -0.05) = 0.1225 Calculate the square root of the right side: 0.35 Break this problem into two subproblems by setting (x + -0.05) equal to 0.35 and -0.35.Subproblem 1
x + -0.05 = 0.35 Simplifying x + -0.05 = 0.35 Reorder the terms: -0.05 + x = 0.35 Solving -0.05 + x = 0.35 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = 0.35 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = 0.35 + 0.05 x = 0.35 + 0.05 Combine like terms: 0.35 + 0.05 = 0.4 x = 0.4 Simplifying x = 0.4Subproblem 2
x + -0.05 = -0.35 Simplifying x + -0.05 = -0.35 Reorder the terms: -0.05 + x = -0.35 Solving -0.05 + x = -0.35 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = -0.35 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = -0.35 + 0.05 x = -0.35 + 0.05 Combine like terms: -0.35 + 0.05 = -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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