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Simplifying 2x2 + -21x + -27 = 0 Reorder the terms: -27 + -21x + 2x2 = 0 Solving -27 + -21x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13.5 + -10.5x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + -10.5x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + -10.5x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + -10.5x + x2 = 0 + 13.5 -10.5x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 -10.5x + x2 = 13.5 The x term is -10.5x. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5x + 27.5625 + x2 = 13.5 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = 13.5 + 27.5625 Combine like terms: 13.5 + 27.5625 = 41.0625 27.5625 + -10.5x + x2 = 41.0625 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 41.0625 Calculate the square root of the right side: 6.408002809 Break this problem into two subproblems by setting (x + -5.25) equal to 6.408002809 and -6.408002809.Subproblem 1
x + -5.25 = 6.408002809 Simplifying x + -5.25 = 6.408002809 Reorder the terms: -5.25 + x = 6.408002809 Solving -5.25 + x = 6.408002809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 6.408002809 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 6.408002809 + 5.25 x = 6.408002809 + 5.25 Combine like terms: 6.408002809 + 5.25 = 11.658002809 x = 11.658002809 Simplifying x = 11.658002809Subproblem 2
x + -5.25 = -6.408002809 Simplifying x + -5.25 = -6.408002809 Reorder the terms: -5.25 + x = -6.408002809 Solving -5.25 + x = -6.408002809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -6.408002809 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -6.408002809 + 5.25 x = -6.408002809 + 5.25 Combine like terms: -6.408002809 + 5.25 = -1.158002809 x = -1.158002809 Simplifying x = -1.158002809Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.658002809, -1.158002809}
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