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Simplifying x2 + 0.17x + -0.039 = 0 Reorder the terms: -0.039 + 0.17x + x2 = 0 Solving -0.039 + 0.17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.039' to each side of the equation. -0.039 + 0.17x + 0.039 + x2 = 0 + 0.039 Reorder the terms: -0.039 + 0.039 + 0.17x + x2 = 0 + 0.039 Combine like terms: -0.039 + 0.039 = 0.000 0.000 + 0.17x + x2 = 0 + 0.039 0.17x + x2 = 0 + 0.039 Combine like terms: 0 + 0.039 = 0.039 0.17x + x2 = 0.039 The x term is 0.17x. Take half its coefficient (0.085). Square it (0.007225) and add it to both sides. Add '0.007225' to each side of the equation. 0.17x + 0.007225 + x2 = 0.039 + 0.007225 Reorder the terms: 0.007225 + 0.17x + x2 = 0.039 + 0.007225 Combine like terms: 0.039 + 0.007225 = 0.046225 0.007225 + 0.17x + x2 = 0.046225 Factor a perfect square on the left side: (x + 0.085)(x + 0.085) = 0.046225 Calculate the square root of the right side: 0.215 Break this problem into two subproblems by setting (x + 0.085) equal to 0.215 and -0.215.Subproblem 1
x + 0.085 = 0.215 Simplifying x + 0.085 = 0.215 Reorder the terms: 0.085 + x = 0.215 Solving 0.085 + x = 0.215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.085' to each side of the equation. 0.085 + -0.085 + x = 0.215 + -0.085 Combine like terms: 0.085 + -0.085 = 0.000 0.000 + x = 0.215 + -0.085 x = 0.215 + -0.085 Combine like terms: 0.215 + -0.085 = 0.13 x = 0.13 Simplifying x = 0.13Subproblem 2
x + 0.085 = -0.215 Simplifying x + 0.085 = -0.215 Reorder the terms: 0.085 + x = -0.215 Solving 0.085 + x = -0.215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.085' to each side of the equation. 0.085 + -0.085 + x = -0.215 + -0.085 Combine like terms: 0.085 + -0.085 = 0.000 0.000 + x = -0.215 + -0.085 x = -0.215 + -0.085 Combine like terms: -0.215 + -0.085 = -0.3 x = -0.3 Simplifying x = -0.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.13, -0.3}
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