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Simplifying 120x2 + 0.12x + 0.03 = 3 + -1x Reorder the terms: 0.03 + 0.12x + 120x2 = 3 + -1x Solving 0.03 + 0.12x + 120x2 = 3 + -1x Solving for variable 'x'. Reorder the terms: 0.03 + -3 + 0.12x + x + 120x2 = 3 + -1x + -3 + x Combine like terms: 0.03 + -3 = -2.97 -2.97 + 0.12x + x + 120x2 = 3 + -1x + -3 + x Combine like terms: 0.12x + x = 1.12x -2.97 + 1.12x + 120x2 = 3 + -1x + -3 + x Reorder the terms: -2.97 + 1.12x + 120x2 = 3 + -3 + -1x + x Combine like terms: 3 + -3 = 0 -2.97 + 1.12x + 120x2 = 0 + -1x + x -2.97 + 1.12x + 120x2 = -1x + x Combine like terms: -1x + x = 0 -2.97 + 1.12x + 120x2 = 0 Begin completing the square. Divide all terms by 120 the coefficient of the squared term: Divide each side by '120'. -0.02475 + 0.009333333333x + x2 = 0 Move the constant term to the right: Add '0.02475' to each side of the equation. -0.02475 + 0.009333333333x + 0.02475 + x2 = 0 + 0.02475 Reorder the terms: -0.02475 + 0.02475 + 0.009333333333x + x2 = 0 + 0.02475 Combine like terms: -0.02475 + 0.02475 = 0.00000 0.00000 + 0.009333333333x + x2 = 0 + 0.02475 0.009333333333x + x2 = 0 + 0.02475 Combine like terms: 0 + 0.02475 = 0.02475 0.009333333333x + x2 = 0.02475 The x term is 0.009333333333x. Take half its coefficient (0.004666666667). Square it (0.00002177777778) and add it to both sides. Add '0.00002177777778' to each side of the equation. 0.009333333333x + 0.00002177777778 + x2 = 0.02475 + 0.00002177777778 Reorder the terms: 0.00002177777778 + 0.009333333333x + x2 = 0.02475 + 0.00002177777778 Combine like terms: 0.02475 + 0.00002177777778 = 0.02477177777778 0.00002177777778 + 0.009333333333x + x2 = 0.02477177777778 Factor a perfect square on the left side: (x + 0.004666666667)(x + 0.004666666667) = 0.02477177777778 Calculate the square root of the right side: 0.157390526 Break this problem into two subproblems by setting (x + 0.004666666667) equal to 0.157390526 and -0.157390526.Subproblem 1
x + 0.004666666667 = 0.157390526 Simplifying x + 0.004666666667 = 0.157390526 Reorder the terms: 0.004666666667 + x = 0.157390526 Solving 0.004666666667 + x = 0.157390526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.004666666667' to each side of the equation. 0.004666666667 + -0.004666666667 + x = 0.157390526 + -0.004666666667 Combine like terms: 0.004666666667 + -0.004666666667 = 0.000000000000 0.000000000000 + x = 0.157390526 + -0.004666666667 x = 0.157390526 + -0.004666666667 Combine like terms: 0.157390526 + -0.004666666667 = 0.152723859333 x = 0.152723859333 Simplifying x = 0.152723859333Subproblem 2
x + 0.004666666667 = -0.157390526 Simplifying x + 0.004666666667 = -0.157390526 Reorder the terms: 0.004666666667 + x = -0.157390526 Solving 0.004666666667 + x = -0.157390526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.004666666667' to each side of the equation. 0.004666666667 + -0.004666666667 + x = -0.157390526 + -0.004666666667 Combine like terms: 0.004666666667 + -0.004666666667 = 0.000000000000 0.000000000000 + x = -0.157390526 + -0.004666666667 x = -0.157390526 + -0.004666666667 Combine like terms: -0.157390526 + -0.004666666667 = -0.162057192667 x = -0.162057192667 Simplifying x = -0.162057192667Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.152723859333, -0.162057192667}
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