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Simplifying 3x2 + 9 = x2 + 27x Reorder the terms: 9 + 3x2 = x2 + 27x Reorder the terms: 9 + 3x2 = 27x + x2 Solving 9 + 3x2 = 27x + x2 Solving for variable 'x'. Reorder the terms: 9 + -27x + 3x2 + -1x2 = 27x + x2 + -27x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 9 + -27x + 2x2 = 27x + x2 + -27x + -1x2 Reorder the terms: 9 + -27x + 2x2 = 27x + -27x + x2 + -1x2 Combine like terms: 27x + -27x = 0 9 + -27x + 2x2 = 0 + x2 + -1x2 9 + -27x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 9 + -27x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + -13.5x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -13.5x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -13.5x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -13.5x + x2 = 0 + -4.5 -13.5x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -13.5x + x2 = -4.5 The x term is -13.5x. Take half its coefficient (-6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. -13.5x + 45.5625 + x2 = -4.5 + 45.5625 Reorder the terms: 45.5625 + -13.5x + x2 = -4.5 + 45.5625 Combine like terms: -4.5 + 45.5625 = 41.0625 45.5625 + -13.5x + x2 = 41.0625 Factor a perfect square on the left side: (x + -6.75)(x + -6.75) = 41.0625 Calculate the square root of the right side: 6.408002809 Break this problem into two subproblems by setting (x + -6.75) equal to 6.408002809 and -6.408002809.Subproblem 1
x + -6.75 = 6.408002809 Simplifying x + -6.75 = 6.408002809 Reorder the terms: -6.75 + x = 6.408002809 Solving -6.75 + x = 6.408002809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = 6.408002809 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = 6.408002809 + 6.75 x = 6.408002809 + 6.75 Combine like terms: 6.408002809 + 6.75 = 13.158002809 x = 13.158002809 Simplifying x = 13.158002809Subproblem 2
x + -6.75 = -6.408002809 Simplifying x + -6.75 = -6.408002809 Reorder the terms: -6.75 + x = -6.408002809 Solving -6.75 + x = -6.408002809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = -6.408002809 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = -6.408002809 + 6.75 x = -6.408002809 + 6.75 Combine like terms: -6.408002809 + 6.75 = 0.341997191 x = 0.341997191 Simplifying x = 0.341997191Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.158002809, 0.341997191}
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