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Simplifying 0.012x2 + -0.1x + -0.18 = 0 Reorder the terms: -0.18 + -0.1x + 0.012x2 = 0 Solving -0.18 + -0.1x + 0.012x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.012 the coefficient of the squared term: Divide each side by '0.012'. -15 + -8.333333333x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -8.333333333x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -8.333333333x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -8.333333333x + x2 = 0 + 15 -8.333333333x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -8.333333333x + x2 = 15 The x term is -8.333333333x. Take half its coefficient (-4.166666667). Square it (17.36111111) and add it to both sides. Add '17.36111111' to each side of the equation. -8.333333333x + 17.36111111 + x2 = 15 + 17.36111111 Reorder the terms: 17.36111111 + -8.333333333x + x2 = 15 + 17.36111111 Combine like terms: 15 + 17.36111111 = 32.36111111 17.36111111 + -8.333333333x + x2 = 32.36111111 Factor a perfect square on the left side: (x + -4.166666667)(x + -4.166666667) = 32.36111111 Calculate the square root of the right side: 5.688682722 Break this problem into two subproblems by setting (x + -4.166666667) equal to 5.688682722 and -5.688682722.Subproblem 1
x + -4.166666667 = 5.688682722 Simplifying x + -4.166666667 = 5.688682722 Reorder the terms: -4.166666667 + x = 5.688682722 Solving -4.166666667 + x = 5.688682722 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = 5.688682722 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = 5.688682722 + 4.166666667 x = 5.688682722 + 4.166666667 Combine like terms: 5.688682722 + 4.166666667 = 9.855349389 x = 9.855349389 Simplifying x = 9.855349389Subproblem 2
x + -4.166666667 = -5.688682722 Simplifying x + -4.166666667 = -5.688682722 Reorder the terms: -4.166666667 + x = -5.688682722 Solving -4.166666667 + x = -5.688682722 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = -5.688682722 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = -5.688682722 + 4.166666667 x = -5.688682722 + 4.166666667 Combine like terms: -5.688682722 + 4.166666667 = -1.522016055 x = -1.522016055 Simplifying x = -1.522016055Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.855349389, -1.522016055}
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