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Simplifying x2 + 0.18x + -0.036 = 0 Reorder the terms: -0.036 + 0.18x + x2 = 0 Solving -0.036 + 0.18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.036' to each side of the equation. -0.036 + 0.18x + 0.036 + x2 = 0 + 0.036 Reorder the terms: -0.036 + 0.036 + 0.18x + x2 = 0 + 0.036 Combine like terms: -0.036 + 0.036 = 0.000 0.000 + 0.18x + x2 = 0 + 0.036 0.18x + x2 = 0 + 0.036 Combine like terms: 0 + 0.036 = 0.036 0.18x + x2 = 0.036 The x term is 0.18x. Take half its coefficient (0.09). Square it (0.0081) and add it to both sides. Add '0.0081' to each side of the equation. 0.18x + 0.0081 + x2 = 0.036 + 0.0081 Reorder the terms: 0.0081 + 0.18x + x2 = 0.036 + 0.0081 Combine like terms: 0.036 + 0.0081 = 0.0441 0.0081 + 0.18x + x2 = 0.0441 Factor a perfect square on the left side: (x + 0.09)(x + 0.09) = 0.0441 Calculate the square root of the right side: 0.21 Break this problem into two subproblems by setting (x + 0.09) equal to 0.21 and -0.21.Subproblem 1
x + 0.09 = 0.21 Simplifying x + 0.09 = 0.21 Reorder the terms: 0.09 + x = 0.21 Solving 0.09 + x = 0.21 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09' to each side of the equation. 0.09 + -0.09 + x = 0.21 + -0.09 Combine like terms: 0.09 + -0.09 = 0.00 0.00 + x = 0.21 + -0.09 x = 0.21 + -0.09 Combine like terms: 0.21 + -0.09 = 0.12 x = 0.12 Simplifying x = 0.12Subproblem 2
x + 0.09 = -0.21 Simplifying x + 0.09 = -0.21 Reorder the terms: 0.09 + x = -0.21 Solving 0.09 + x = -0.21 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09' to each side of the equation. 0.09 + -0.09 + x = -0.21 + -0.09 Combine like terms: 0.09 + -0.09 = 0.00 0.00 + x = -0.21 + -0.09 x = -0.21 + -0.09 Combine like terms: -0.21 + -0.09 = -0.3 x = -0.3 Simplifying x = -0.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.12, -0.3}
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