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Simplifying 6x2 + -9x + -293 = 0 Reorder the terms: -293 + -9x + 6x2 = 0 Solving -293 + -9x + 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'. -48.83333333 + -1.5x + x2 = 0 Move the constant term to the right: Add '48.83333333' to each side of the equation. -48.83333333 + -1.5x + 48.83333333 + x2 = 0 + 48.83333333 Reorder the terms: -48.83333333 + 48.83333333 + -1.5x + x2 = 0 + 48.83333333 Combine like terms: -48.83333333 + 48.83333333 = 0.00000000 0.00000000 + -1.5x + x2 = 0 + 48.83333333 -1.5x + x2 = 0 + 48.83333333 Combine like terms: 0 + 48.83333333 = 48.83333333 -1.5x + x2 = 48.83333333 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 48.83333333 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 48.83333333 + 0.5625 Combine like terms: 48.83333333 + 0.5625 = 49.39583333 0.5625 + -1.5x + x2 = 49.39583333 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 49.39583333 Calculate the square root of the right side: 7.028216938 Break this problem into two subproblems by setting (x + -0.75) equal to 7.028216938 and -7.028216938.Subproblem 1
x + -0.75 = 7.028216938 Simplifying x + -0.75 = 7.028216938 Reorder the terms: -0.75 + x = 7.028216938 Solving -0.75 + x = 7.028216938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 7.028216938 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 7.028216938 + 0.75 x = 7.028216938 + 0.75 Combine like terms: 7.028216938 + 0.75 = 7.778216938 x = 7.778216938 Simplifying x = 7.778216938Subproblem 2
x + -0.75 = -7.028216938 Simplifying x + -0.75 = -7.028216938 Reorder the terms: -0.75 + x = -7.028216938 Solving -0.75 + x = -7.028216938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -7.028216938 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -7.028216938 + 0.75 x = -7.028216938 + 0.75 Combine like terms: -7.028216938 + 0.75 = -6.278216938 x = -6.278216938 Simplifying x = -6.278216938Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.778216938, -6.278216938}
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