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Simplifying 0.09x2 + -2.007x + 0.00012 = 0 Reorder the terms: 0.00012 + -2.007x + 0.09x2 = 0 Solving 0.00012 + -2.007x + 0.09x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.09 the coefficient of the squared term: Divide each side by '0.09'. 0.001333333333 + -22.3x + x2 = 0 Move the constant term to the right: Add '-0.001333333333' to each side of the equation. 0.001333333333 + -22.3x + -0.001333333333 + x2 = 0 + -0.001333333333 Reorder the terms: 0.001333333333 + -0.001333333333 + -22.3x + x2 = 0 + -0.001333333333 Combine like terms: 0.001333333333 + -0.001333333333 = 0.000000000000 0.000000000000 + -22.3x + x2 = 0 + -0.001333333333 -22.3x + x2 = 0 + -0.001333333333 Combine like terms: 0 + -0.001333333333 = -0.001333333333 -22.3x + x2 = -0.001333333333 The x term is -22.3x. Take half its coefficient (-11.15). Square it (124.3225) and add it to both sides. Add '124.3225' to each side of the equation. -22.3x + 124.3225 + x2 = -0.001333333333 + 124.3225 Reorder the terms: 124.3225 + -22.3x + x2 = -0.001333333333 + 124.3225 Combine like terms: -0.001333333333 + 124.3225 = 124.321166666667 124.3225 + -22.3x + x2 = 124.321166666667 Factor a perfect square on the left side: (x + -11.15)(x + -11.15) = 124.321166666667 Calculate the square root of the right side: 11.149940209 Break this problem into two subproblems by setting (x + -11.15) equal to 11.149940209 and -11.149940209.Subproblem 1
x + -11.15 = 11.149940209 Simplifying x + -11.15 = 11.149940209 Reorder the terms: -11.15 + x = 11.149940209 Solving -11.15 + x = 11.149940209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.15' to each side of the equation. -11.15 + 11.15 + x = 11.149940209 + 11.15 Combine like terms: -11.15 + 11.15 = 0.00 0.00 + x = 11.149940209 + 11.15 x = 11.149940209 + 11.15 Combine like terms: 11.149940209 + 11.15 = 22.299940209 x = 22.299940209 Simplifying x = 22.299940209Subproblem 2
x + -11.15 = -11.149940209 Simplifying x + -11.15 = -11.149940209 Reorder the terms: -11.15 + x = -11.149940209 Solving -11.15 + x = -11.149940209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.15' to each side of the equation. -11.15 + 11.15 + x = -11.149940209 + 11.15 Combine like terms: -11.15 + 11.15 = 0.00 0.00 + x = -11.149940209 + 11.15 x = -11.149940209 + 11.15 Combine like terms: -11.149940209 + 11.15 = 0.000059791 x = 0.000059791 Simplifying x = 0.000059791Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.299940209, 0.000059791}
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