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Simplifying -900x2 + 300x + 71 = 0 Reorder the terms: 71 + 300x + -900x2 = 0 Solving 71 + 300x + -900x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -900 the coefficient of the squared term: Divide each side by '-900'. -0.07888888889 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.07888888889' to each side of the equation. -0.07888888889 + -0.3333333333x + 0.07888888889 + x2 = 0 + 0.07888888889 Reorder the terms: -0.07888888889 + 0.07888888889 + -0.3333333333x + x2 = 0 + 0.07888888889 Combine like terms: -0.07888888889 + 0.07888888889 = 0.00000000000 0.00000000000 + -0.3333333333x + x2 = 0 + 0.07888888889 -0.3333333333x + x2 = 0 + 0.07888888889 Combine like terms: 0 + 0.07888888889 = 0.07888888889 -0.3333333333x + x2 = 0.07888888889 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 = 0.07888888889 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 0.07888888889 + 0.02777777779 Combine like terms: 0.07888888889 + 0.02777777779 = 0.10666666668 0.02777777779 + -0.3333333333x + x2 = 0.10666666668 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 0.10666666668 Calculate the square root of the right side: 0.326598632 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 0.326598632 and -0.326598632.Subproblem 1
x + -0.1666666667 = 0.326598632 Simplifying x + -0.1666666667 = 0.326598632 Reorder the terms: -0.1666666667 + x = 0.326598632 Solving -0.1666666667 + x = 0.326598632 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 = 0.326598632 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 0.326598632 + 0.1666666667 x = 0.326598632 + 0.1666666667 Combine like terms: 0.326598632 + 0.1666666667 = 0.4932652987 x = 0.4932652987 Simplifying x = 0.4932652987Subproblem 2
x + -0.1666666667 = -0.326598632 Simplifying x + -0.1666666667 = -0.326598632 Reorder the terms: -0.1666666667 + x = -0.326598632 Solving -0.1666666667 + x = -0.326598632 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 = -0.326598632 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -0.326598632 + 0.1666666667 x = -0.326598632 + 0.1666666667 Combine like terms: -0.326598632 + 0.1666666667 = -0.1599319653 x = -0.1599319653 Simplifying x = -0.1599319653Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4932652987, -0.1599319653}
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