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Simplifying 0 = x2 + 0.036x + -0.00693 Reorder the terms: 0 = -0.00693 + 0.036x + x2 Solving 0 = -0.00693 + 0.036x + x2 Solving for variable 'x'. Combine like terms: 0 + 0.00693 = 0.00693 0.00693 + -0.036x + -1x2 = -0.00693 + 0.036x + x2 + 0.00693 + -0.036x + -1x2 Reorder the terms: 0.00693 + -0.036x + -1x2 = -0.00693 + 0.00693 + 0.036x + -0.036x + x2 + -1x2 Combine like terms: -0.00693 + 0.00693 = 0.00000 0.00693 + -0.036x + -1x2 = 0.00000 + 0.036x + -0.036x + x2 + -1x2 0.00693 + -0.036x + -1x2 = 0.036x + -0.036x + x2 + -1x2 Combine like terms: 0.036x + -0.036x = 0.000 0.00693 + -0.036x + -1x2 = 0.000 + x2 + -1x2 0.00693 + -0.036x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.00693 + -0.036x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.00693 + 0.036x + x2 = 0 Move the constant term to the right: Add '0.00693' to each side of the equation. -0.00693 + 0.036x + 0.00693 + x2 = 0 + 0.00693 Reorder the terms: -0.00693 + 0.00693 + 0.036x + x2 = 0 + 0.00693 Combine like terms: -0.00693 + 0.00693 = 0.00000 0.00000 + 0.036x + x2 = 0 + 0.00693 0.036x + x2 = 0 + 0.00693 Combine like terms: 0 + 0.00693 = 0.00693 0.036x + x2 = 0.00693 The x term is 0.036x. Take half its coefficient (0.018). Square it (0.000324) and add it to both sides. Add '0.000324' to each side of the equation. 0.036x + 0.000324 + x2 = 0.00693 + 0.000324 Reorder the terms: 0.000324 + 0.036x + x2 = 0.00693 + 0.000324 Combine like terms: 0.00693 + 0.000324 = 0.007254 0.000324 + 0.036x + x2 = 0.007254 Factor a perfect square on the left side: (x + 0.018)(x + 0.018) = 0.007254 Calculate the square root of the right side: 0.085170417 Break this problem into two subproblems by setting (x + 0.018) equal to 0.085170417 and -0.085170417.Subproblem 1
x + 0.018 = 0.085170417 Simplifying x + 0.018 = 0.085170417 Reorder the terms: 0.018 + x = 0.085170417 Solving 0.018 + x = 0.085170417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.018' to each side of the equation. 0.018 + -0.018 + x = 0.085170417 + -0.018 Combine like terms: 0.018 + -0.018 = 0.000 0.000 + x = 0.085170417 + -0.018 x = 0.085170417 + -0.018 Combine like terms: 0.085170417 + -0.018 = 0.067170417 x = 0.067170417 Simplifying x = 0.067170417Subproblem 2
x + 0.018 = -0.085170417 Simplifying x + 0.018 = -0.085170417 Reorder the terms: 0.018 + x = -0.085170417 Solving 0.018 + x = -0.085170417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.018' to each side of the equation. 0.018 + -0.018 + x = -0.085170417 + -0.018 Combine like terms: 0.018 + -0.018 = 0.000 0.000 + x = -0.085170417 + -0.018 x = -0.085170417 + -0.018 Combine like terms: -0.085170417 + -0.018 = -0.103170417 x = -0.103170417 Simplifying x = -0.103170417Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.067170417, -0.103170417}
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