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Simplifying x2 + 0.12x + -0.054 = 0 Reorder the terms: -0.054 + 0.12x + x2 = 0 Solving -0.054 + 0.12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.054' to each side of the equation. -0.054 + 0.12x + 0.054 + x2 = 0 + 0.054 Reorder the terms: -0.054 + 0.054 + 0.12x + x2 = 0 + 0.054 Combine like terms: -0.054 + 0.054 = 0.000 0.000 + 0.12x + x2 = 0 + 0.054 0.12x + x2 = 0 + 0.054 Combine like terms: 0 + 0.054 = 0.054 0.12x + x2 = 0.054 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 = 0.054 + 0.0036 Reorder the terms: 0.0036 + 0.12x + x2 = 0.054 + 0.0036 Combine like terms: 0.054 + 0.0036 = 0.0576 0.0036 + 0.12x + x2 = 0.0576 Factor a perfect square on the left side: (x + 0.06)(x + 0.06) = 0.0576 Calculate the square root of the right side: 0.24 Break this problem into two subproblems by setting (x + 0.06) equal to 0.24 and -0.24.Subproblem 1
x + 0.06 = 0.24 Simplifying x + 0.06 = 0.24 Reorder the terms: 0.06 + x = 0.24 Solving 0.06 + x = 0.24 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 = 0.24 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = 0.24 + -0.06 x = 0.24 + -0.06 Combine like terms: 0.24 + -0.06 = 0.18 x = 0.18 Simplifying x = 0.18Subproblem 2
x + 0.06 = -0.24 Simplifying x + 0.06 = -0.24 Reorder the terms: 0.06 + x = -0.24 Solving 0.06 + x = -0.24 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 = -0.24 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = -0.24 + -0.06 x = -0.24 + -0.06 Combine like terms: -0.24 + -0.06 = -0.3 x = -0.3 Simplifying x = -0.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.18, -0.3}
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