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Simplifying 1.9964x2 + 0.0072x + -0.0036 = 0 Reorder the terms: -0.0036 + 0.0072x + 1.9964x2 = 0 Solving -0.0036 + 0.0072x + 1.9964x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.9964 the coefficient of the squared term: Divide each side by '1.9964'. -0.001803245843 + 0.003606491685x + x2 = 0 Move the constant term to the right: Add '0.001803245843' to each side of the equation. -0.001803245843 + 0.003606491685x + 0.001803245843 + x2 = 0 + 0.001803245843 Reorder the terms: -0.001803245843 + 0.001803245843 + 0.003606491685x + x2 = 0 + 0.001803245843 Combine like terms: -0.001803245843 + 0.001803245843 = 0.000000000000 0.000000000000 + 0.003606491685x + x2 = 0 + 0.001803245843 0.003606491685x + x2 = 0 + 0.001803245843 Combine like terms: 0 + 0.001803245843 = 0.001803245843 0.003606491685x + x2 = 0.001803245843 The x term is 0.003606491685x. Take half its coefficient (0.001803245843). Square it (0.000003251695570) and add it to both sides. Add '0.000003251695570' to each side of the equation. 0.003606491685x + 0.000003251695570 + x2 = 0.001803245843 + 0.000003251695570 Reorder the terms: 0.000003251695570 + 0.003606491685x + x2 = 0.001803245843 + 0.000003251695570 Combine like terms: 0.001803245843 + 0.000003251695570 = 0.00180649753857 0.000003251695570 + 0.003606491685x + x2 = 0.00180649753857 Factor a perfect square on the left side: (x + 0.001803245843)(x + 0.001803245843) = 0.00180649753857 Calculate the square root of the right side: 0.042502912 Break this problem into two subproblems by setting (x + 0.001803245843) equal to 0.042502912 and -0.042502912.Subproblem 1
x + 0.001803245843 = 0.042502912 Simplifying x + 0.001803245843 = 0.042502912 Reorder the terms: 0.001803245843 + x = 0.042502912 Solving 0.001803245843 + x = 0.042502912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.001803245843' to each side of the equation. 0.001803245843 + -0.001803245843 + x = 0.042502912 + -0.001803245843 Combine like terms: 0.001803245843 + -0.001803245843 = 0.000000000000 0.000000000000 + x = 0.042502912 + -0.001803245843 x = 0.042502912 + -0.001803245843 Combine like terms: 0.042502912 + -0.001803245843 = 0.040699666157 x = 0.040699666157 Simplifying x = 0.040699666157Subproblem 2
x + 0.001803245843 = -0.042502912 Simplifying x + 0.001803245843 = -0.042502912 Reorder the terms: 0.001803245843 + x = -0.042502912 Solving 0.001803245843 + x = -0.042502912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.001803245843' to each side of the equation. 0.001803245843 + -0.001803245843 + x = -0.042502912 + -0.001803245843 Combine like terms: 0.001803245843 + -0.001803245843 = 0.000000000000 0.000000000000 + x = -0.042502912 + -0.001803245843 x = -0.042502912 + -0.001803245843 Combine like terms: -0.042502912 + -0.001803245843 = -0.044306157843 x = -0.044306157843 Simplifying x = -0.044306157843Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.040699666157, -0.044306157843}
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