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Simplifying 6x * x + -1x + -300 = 0 Multiply x * x 6x2 + -1x + -300 = 0 Reorder the terms: -300 + -1x + 6x2 = 0 Solving -300 + -1x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -50 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -0.1666666667x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -0.1666666667x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -0.1666666667x + x2 = 0 + 50 -0.1666666667x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -0.1666666667x + x2 = 50 The x term is -0.1666666667x. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667x + 0.006944444447 + x2 = 50 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 50 + 0.006944444447 Combine like terms: 50 + 0.006944444447 = 50.006944444447 0.006944444447 + -0.1666666667x + x2 = 50.006944444447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 50.006944444447 Calculate the square root of the right side: 7.071558841 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 7.071558841 and -7.071558841.Subproblem 1
x + -0.08333333335 = 7.071558841 Simplifying x + -0.08333333335 = 7.071558841 Reorder the terms: -0.08333333335 + x = 7.071558841 Solving -0.08333333335 + x = 7.071558841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = 7.071558841 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 7.071558841 + 0.08333333335 x = 7.071558841 + 0.08333333335 Combine like terms: 7.071558841 + 0.08333333335 = 7.15489217435 x = 7.15489217435 Simplifying x = 7.15489217435Subproblem 2
x + -0.08333333335 = -7.071558841 Simplifying x + -0.08333333335 = -7.071558841 Reorder the terms: -0.08333333335 + x = -7.071558841 Solving -0.08333333335 + x = -7.071558841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = -7.071558841 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -7.071558841 + 0.08333333335 x = -7.071558841 + 0.08333333335 Combine like terms: -7.071558841 + 0.08333333335 = -6.98822550765 x = -6.98822550765 Simplifying x = -6.98822550765Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.15489217435, -6.98822550765}
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