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Simplifying x2 + 0.12x + -0.0156 = 0 Reorder the terms: -0.0156 + 0.12x + x2 = 0 Solving -0.0156 + 0.12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.0156' to each side of the equation. -0.0156 + 0.12x + 0.0156 + x2 = 0 + 0.0156 Reorder the terms: -0.0156 + 0.0156 + 0.12x + x2 = 0 + 0.0156 Combine like terms: -0.0156 + 0.0156 = 0.0000 0.0000 + 0.12x + x2 = 0 + 0.0156 0.12x + x2 = 0 + 0.0156 Combine like terms: 0 + 0.0156 = 0.0156 0.12x + x2 = 0.0156 The x term is 0.12x. Take half its coefficient (0.06). Square it (0.0036) and add it to both sides. Add '0.0036' to each side of the equation. 0.12x + 0.0036 + x2 = 0.0156 + 0.0036 Reorder the terms: 0.0036 + 0.12x + x2 = 0.0156 + 0.0036 Combine like terms: 0.0156 + 0.0036 = 0.0192 0.0036 + 0.12x + x2 = 0.0192 Factor a perfect square on the left side: (x + 0.06)(x + 0.06) = 0.0192 Calculate the square root of the right side: 0.138564065 Break this problem into two subproblems by setting (x + 0.06) equal to 0.138564065 and -0.138564065.Subproblem 1
x + 0.06 = 0.138564065 Simplifying x + 0.06 = 0.138564065 Reorder the terms: 0.06 + x = 0.138564065 Solving 0.06 + x = 0.138564065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06' to each side of the equation. 0.06 + -0.06 + x = 0.138564065 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = 0.138564065 + -0.06 x = 0.138564065 + -0.06 Combine like terms: 0.138564065 + -0.06 = 0.078564065 x = 0.078564065 Simplifying x = 0.078564065Subproblem 2
x + 0.06 = -0.138564065 Simplifying x + 0.06 = -0.138564065 Reorder the terms: 0.06 + x = -0.138564065 Solving 0.06 + x = -0.138564065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06' to each side of the equation. 0.06 + -0.06 + x = -0.138564065 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = -0.138564065 + -0.06 x = -0.138564065 + -0.06 Combine like terms: -0.138564065 + -0.06 = -0.198564065 x = -0.198564065 Simplifying x = -0.198564065Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.078564065, -0.198564065}
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