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Simplifying 6x2 + -6x = 89 Reorder the terms: -6x + 6x2 = 89 Solving -6x + 6x2 = 89 Solving for variable 'x'. Reorder the terms: -89 + -6x + 6x2 = 89 + -89 Combine like terms: 89 + -89 = 0 -89 + -6x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -14.83333333 + -1x + x2 = 0 Move the constant term to the right: Add '14.83333333' to each side of the equation. -14.83333333 + -1x + 14.83333333 + x2 = 0 + 14.83333333 Reorder the terms: -14.83333333 + 14.83333333 + -1x + x2 = 0 + 14.83333333 Combine like terms: -14.83333333 + 14.83333333 = 0.00000000 0.00000000 + -1x + x2 = 0 + 14.83333333 -1x + x2 = 0 + 14.83333333 Combine like terms: 0 + 14.83333333 = 14.83333333 -1x + x2 = 14.83333333 The x term is -1x. 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. -1x + 0.25 + x2 = 14.83333333 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 14.83333333 + 0.25 Combine like terms: 14.83333333 + 0.25 = 15.08333333 0.25 + -1x + x2 = 15.08333333 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 15.08333333 Calculate the square root of the right side: 3.883726732 Break this problem into two subproblems by setting (x + -0.5) equal to 3.883726732 and -3.883726732.Subproblem 1
x + -0.5 = 3.883726732 Simplifying x + -0.5 = 3.883726732 Reorder the terms: -0.5 + x = 3.883726732 Solving -0.5 + x = 3.883726732 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 = 3.883726732 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.883726732 + 0.5 x = 3.883726732 + 0.5 Combine like terms: 3.883726732 + 0.5 = 4.383726732 x = 4.383726732 Simplifying x = 4.383726732Subproblem 2
x + -0.5 = -3.883726732 Simplifying x + -0.5 = -3.883726732 Reorder the terms: -0.5 + x = -3.883726732 Solving -0.5 + x = -3.883726732 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 = -3.883726732 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.883726732 + 0.5 x = -3.883726732 + 0.5 Combine like terms: -3.883726732 + 0.5 = -3.383726732 x = -3.383726732 Simplifying x = -3.383726732Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.383726732, -3.383726732}
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