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Simplifying x2 + 0.0013489x + -0.004114 = 0 Reorder the terms: -0.004114 + 0.0013489x + x2 = 0 Solving -0.004114 + 0.0013489x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.004114' to each side of the equation. -0.004114 + 0.0013489x + 0.004114 + x2 = 0 + 0.004114 Reorder the terms: -0.004114 + 0.004114 + 0.0013489x + x2 = 0 + 0.004114 Combine like terms: -0.004114 + 0.004114 = 0.000000 0.000000 + 0.0013489x + x2 = 0 + 0.004114 0.0013489x + x2 = 0 + 0.004114 Combine like terms: 0 + 0.004114 = 0.004114 0.0013489x + x2 = 0.004114 The x term is 0.0013489x. Take half its coefficient (0.00067445). Square it (0.0000004548828025) and add it to both sides. Add '0.0000004548828025' to each side of the equation. 0.0013489x + 0.0000004548828025 + x2 = 0.004114 + 0.0000004548828025 Reorder the terms: 0.0000004548828025 + 0.0013489x + x2 = 0.004114 + 0.0000004548828025 Combine like terms: 0.004114 + 0.0000004548828025 = 0.0041144548828025 0.0000004548828025 + 0.0013489x + x2 = 0.0041144548828025 Factor a perfect square on the left side: (x + 0.00067445)(x + 0.00067445) = 0.0041144548828025 Calculate the square root of the right side: 0.064144017 Break this problem into two subproblems by setting (x + 0.00067445) equal to 0.064144017 and -0.064144017.Subproblem 1
x + 0.00067445 = 0.064144017 Simplifying x + 0.00067445 = 0.064144017 Reorder the terms: 0.00067445 + x = 0.064144017 Solving 0.00067445 + x = 0.064144017 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00067445' to each side of the equation. 0.00067445 + -0.00067445 + x = 0.064144017 + -0.00067445 Combine like terms: 0.00067445 + -0.00067445 = 0.00000000 0.00000000 + x = 0.064144017 + -0.00067445 x = 0.064144017 + -0.00067445 Combine like terms: 0.064144017 + -0.00067445 = 0.063469567 x = 0.063469567 Simplifying x = 0.063469567Subproblem 2
x + 0.00067445 = -0.064144017 Simplifying x + 0.00067445 = -0.064144017 Reorder the terms: 0.00067445 + x = -0.064144017 Solving 0.00067445 + x = -0.064144017 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00067445' to each side of the equation. 0.00067445 + -0.00067445 + x = -0.064144017 + -0.00067445 Combine like terms: 0.00067445 + -0.00067445 = 0.00000000 0.00000000 + x = -0.064144017 + -0.00067445 x = -0.064144017 + -0.00067445 Combine like terms: -0.064144017 + -0.00067445 = -0.064818467 x = -0.064818467 Simplifying x = -0.064818467Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.063469567, -0.064818467}
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