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Simplifying 3x2 + -1x = 45 Reorder the terms: -1x + 3x2 = 45 Solving -1x + 3x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + -1x + 3x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + -1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -15 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -0.3333333333x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -0.3333333333x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -0.3333333333x + x2 = 0 + 15 -0.3333333333x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -0.3333333333x + x2 = 15 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 15 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 15 + 0.02777777779 Combine like terms: 15 + 0.02777777779 = 15.02777777779 0.02777777779 + -0.3333333333x + x2 = 15.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 15.02777777779 Calculate the square root of the right side: 3.876567783 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 3.876567783 and -3.876567783.Subproblem 1
x + -0.1666666667 = 3.876567783 Simplifying x + -0.1666666667 = 3.876567783 Reorder the terms: -0.1666666667 + x = 3.876567783 Solving -0.1666666667 + x = 3.876567783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 3.876567783 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 3.876567783 + 0.1666666667 x = 3.876567783 + 0.1666666667 Combine like terms: 3.876567783 + 0.1666666667 = 4.0432344497 x = 4.0432344497 Simplifying x = 4.0432344497Subproblem 2
x + -0.1666666667 = -3.876567783 Simplifying x + -0.1666666667 = -3.876567783 Reorder the terms: -0.1666666667 + x = -3.876567783 Solving -0.1666666667 + x = -3.876567783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -3.876567783 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -3.876567783 + 0.1666666667 x = -3.876567783 + 0.1666666667 Combine like terms: -3.876567783 + 0.1666666667 = -3.7099011163 x = -3.7099011163 Simplifying x = -3.7099011163Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.0432344497, -3.7099011163}
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