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Simplifying 6x2 = 459 + -27x Solving 6x2 = 459 + -27x Solving for variable 'x'. Reorder the terms: -459 + 27x + 6x2 = 459 + -27x + -459 + 27x Reorder the terms: -459 + 27x + 6x2 = 459 + -459 + -27x + 27x Combine like terms: 459 + -459 = 0 -459 + 27x + 6x2 = 0 + -27x + 27x -459 + 27x + 6x2 = -27x + 27x Combine like terms: -27x + 27x = 0 -459 + 27x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-153 + 9x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-153 + 9x + 2x2)' equal to zero and attempt to solve: Simplifying -153 + 9x + 2x2 = 0 Solving -153 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -76.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '76.5' to each side of the equation. -76.5 + 4.5x + 76.5 + x2 = 0 + 76.5 Reorder the terms: -76.5 + 76.5 + 4.5x + x2 = 0 + 76.5 Combine like terms: -76.5 + 76.5 = 0.0 0.0 + 4.5x + x2 = 0 + 76.5 4.5x + x2 = 0 + 76.5 Combine like terms: 0 + 76.5 = 76.5 4.5x + x2 = 76.5 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 76.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 76.5 + 5.0625 Combine like terms: 76.5 + 5.0625 = 81.5625 5.0625 + 4.5x + x2 = 81.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 81.5625 Calculate the square root of the right side: 9.031195934 Break this problem into two subproblems by setting (x + 2.25) equal to 9.031195934 and -9.031195934.Subproblem 1
x + 2.25 = 9.031195934 Simplifying x + 2.25 = 9.031195934 Reorder the terms: 2.25 + x = 9.031195934 Solving 2.25 + x = 9.031195934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 9.031195934 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 9.031195934 + -2.25 x = 9.031195934 + -2.25 Combine like terms: 9.031195934 + -2.25 = 6.781195934 x = 6.781195934 Simplifying x = 6.781195934Subproblem 2
x + 2.25 = -9.031195934 Simplifying x + 2.25 = -9.031195934 Reorder the terms: 2.25 + x = -9.031195934 Solving 2.25 + x = -9.031195934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -9.031195934 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -9.031195934 + -2.25 x = -9.031195934 + -2.25 Combine like terms: -9.031195934 + -2.25 = -11.281195934 x = -11.281195934 Simplifying x = -11.281195934Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.781195934, -11.281195934}Solution
x = {6.781195934, -11.281195934}
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