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Simplifying 6x2 + x + -50 = 600 Reorder the terms: -50 + x + 6x2 = 600 Solving -50 + x + 6x2 = 600 Solving for variable 'x'. Reorder the terms: -50 + -600 + x + 6x2 = 600 + -600 Combine like terms: -50 + -600 = -650 -650 + x + 6x2 = 600 + -600 Combine like terms: 600 + -600 = 0 -650 + x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -108.3333333 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '108.3333333' to each side of the equation. -108.3333333 + 0.1666666667x + 108.3333333 + x2 = 0 + 108.3333333 Reorder the terms: -108.3333333 + 108.3333333 + 0.1666666667x + x2 = 0 + 108.3333333 Combine like terms: -108.3333333 + 108.3333333 = 0.0000000 0.0000000 + 0.1666666667x + x2 = 0 + 108.3333333 0.1666666667x + x2 = 0 + 108.3333333 Combine like terms: 0 + 108.3333333 = 108.3333333 0.1666666667x + x2 = 108.3333333 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 = 108.3333333 + 0.25 Reorder the terms: 0.25 + 0.1666666667x + x2 = 108.3333333 + 0.25 Combine like terms: 108.3333333 + 0.25 = 108.5833333 0.25 + 0.1666666667x + x2 = 108.5833333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 108.5833333 Calculate the square root of the right side: 10.420332687 Break this problem into two subproblems by setting (x + 0.5) equal to 10.420332687 and -10.420332687.Subproblem 1
x + 0.5 = 10.420332687 Simplifying x + 0.5 = 10.420332687 Reorder the terms: 0.5 + x = 10.420332687 Solving 0.5 + x = 10.420332687 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 = 10.420332687 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 10.420332687 + -0.5 x = 10.420332687 + -0.5 Combine like terms: 10.420332687 + -0.5 = 9.920332687 x = 9.920332687 Simplifying x = 9.920332687Subproblem 2
x + 0.5 = -10.420332687 Simplifying x + 0.5 = -10.420332687 Reorder the terms: 0.5 + x = -10.420332687 Solving 0.5 + x = -10.420332687 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 = -10.420332687 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -10.420332687 + -0.5 x = -10.420332687 + -0.5 Combine like terms: -10.420332687 + -0.5 = -10.920332687 x = -10.920332687 Simplifying x = -10.920332687Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.920332687, -10.920332687}
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