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Simplifying 6x2 + 18x = 216 Reorder the terms: 18x + 6x2 = 216 Solving 18x + 6x2 = 216 Solving for variable 'x'. Reorder the terms: -216 + 18x + 6x2 = 216 + -216 Combine like terms: 216 + -216 = 0 -216 + 18x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-36 + 3x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-36 + 3x + x2)' equal to zero and attempt to solve: Simplifying -36 + 3x + x2 = 0 Solving -36 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 3x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 3x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 3x + x2 = 0 + 36 3x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 3x + x2 = 36 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 36 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 36 + 2.25 Combine like terms: 36 + 2.25 = 38.25 2.25 + 3x + x2 = 38.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (x + 1.5) equal to 6.184658438 and -6.184658438.Subproblem 1
x + 1.5 = 6.184658438 Simplifying x + 1.5 = 6.184658438 Reorder the terms: 1.5 + x = 6.184658438 Solving 1.5 + x = 6.184658438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 6.184658438 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 6.184658438 + -1.5 x = 6.184658438 + -1.5 Combine like terms: 6.184658438 + -1.5 = 4.684658438 x = 4.684658438 Simplifying x = 4.684658438Subproblem 2
x + 1.5 = -6.184658438 Simplifying x + 1.5 = -6.184658438 Reorder the terms: 1.5 + x = -6.184658438 Solving 1.5 + x = -6.184658438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -6.184658438 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -6.184658438 + -1.5 x = -6.184658438 + -1.5 Combine like terms: -6.184658438 + -1.5 = -7.684658438 x = -7.684658438 Simplifying x = -7.684658438Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.684658438, -7.684658438}Solution
x = {4.684658438, -7.684658438}
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