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Simplifying 0 = 6x2 + -1x + -50 Reorder the terms: 0 = -50 + -1x + 6x2 Solving 0 = -50 + -1x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 50 = 50 50 + x + -6x2 = -50 + -1x + 6x2 + 50 + x + -6x2 Reorder the terms: 50 + x + -6x2 = -50 + 50 + -1x + x + 6x2 + -6x2 Combine like terms: -50 + 50 = 0 50 + x + -6x2 = 0 + -1x + x + 6x2 + -6x2 50 + x + -6x2 = -1x + x + 6x2 + -6x2 Combine like terms: -1x + x = 0 50 + x + -6x2 = 0 + 6x2 + -6x2 50 + x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 50 + x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -8.333333333 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '8.333333333' to each side of the equation. -8.333333333 + -0.1666666667x + 8.333333333 + x2 = 0 + 8.333333333 Reorder the terms: -8.333333333 + 8.333333333 + -0.1666666667x + x2 = 0 + 8.333333333 Combine like terms: -8.333333333 + 8.333333333 = 0.000000000 0.000000000 + -0.1666666667x + x2 = 0 + 8.333333333 -0.1666666667x + x2 = 0 + 8.333333333 Combine like terms: 0 + 8.333333333 = 8.333333333 -0.1666666667x + x2 = 8.333333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.1666666667x + 0.25 + x2 = 8.333333333 + 0.25 Reorder the terms: 0.25 + -0.1666666667x + x2 = 8.333333333 + 0.25 Combine like terms: 8.333333333 + 0.25 = 8.583333333 0.25 + -0.1666666667x + x2 = 8.583333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 8.583333333 Calculate the square root of the right side: 2.929732638 Break this problem into two subproblems by setting (x + 0.5) equal to 2.929732638 and -2.929732638.Subproblem 1
x + 0.5 = 2.929732638 Simplifying x + 0.5 = 2.929732638 Reorder the terms: 0.5 + x = 2.929732638 Solving 0.5 + x = 2.929732638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.929732638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.929732638 + -0.5 x = 2.929732638 + -0.5 Combine like terms: 2.929732638 + -0.5 = 2.429732638 x = 2.429732638 Simplifying x = 2.429732638Subproblem 2
x + 0.5 = -2.929732638 Simplifying x + 0.5 = -2.929732638 Reorder the terms: 0.5 + x = -2.929732638 Solving 0.5 + x = -2.929732638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.929732638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.929732638 + -0.5 x = -2.929732638 + -0.5 Combine like terms: -2.929732638 + -0.5 = -3.429732638 x = -3.429732638 Simplifying x = -3.429732638Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.429732638, -3.429732638}
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