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Simplifying 3x2 + 9x = 27 Reorder the terms: 9x + 3x2 = 27 Solving 9x + 3x2 = 27 Solving for variable 'x'. Reorder the terms: -27 + 9x + 3x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 9x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + 3x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-9 + 3x + x2)' equal to zero and attempt to solve: Simplifying -9 + 3x + x2 = 0 Solving -9 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 3x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 3x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 3x + x2 = 0 + 9 3x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 3x + x2 = 9 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 = 9 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 9 + 2.25 Combine like terms: 9 + 2.25 = 11.25 2.25 + 3x + x2 = 11.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x + 1.5) equal to 3.354101966 and -3.354101966.Subproblem 1
x + 1.5 = 3.354101966 Simplifying x + 1.5 = 3.354101966 Reorder the terms: 1.5 + x = 3.354101966 Solving 1.5 + x = 3.354101966 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 = 3.354101966 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.354101966 + -1.5 x = 3.354101966 + -1.5 Combine like terms: 3.354101966 + -1.5 = 1.854101966 x = 1.854101966 Simplifying x = 1.854101966Subproblem 2
x + 1.5 = -3.354101966 Simplifying x + 1.5 = -3.354101966 Reorder the terms: 1.5 + x = -3.354101966 Solving 1.5 + x = -3.354101966 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 = -3.354101966 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.354101966 + -1.5 x = -3.354101966 + -1.5 Combine like terms: -3.354101966 + -1.5 = -4.854101966 x = -4.854101966 Simplifying x = -4.854101966Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.854101966, -4.854101966}Solution
x = {1.854101966, -4.854101966}
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