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Simplifying 3x2 + 9x + -456 = 0 Reorder the terms: -456 + 9x + 3x2 = 0 Solving -456 + 9x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-152 + 3x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-152 + 3x + x2)' equal to zero and attempt to solve: Simplifying -152 + 3x + x2 = 0 Solving -152 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '152' to each side of the equation. -152 + 3x + 152 + x2 = 0 + 152 Reorder the terms: -152 + 152 + 3x + x2 = 0 + 152 Combine like terms: -152 + 152 = 0 0 + 3x + x2 = 0 + 152 3x + x2 = 0 + 152 Combine like terms: 0 + 152 = 152 3x + x2 = 152 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 = 152 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 152 + 2.25 Combine like terms: 152 + 2.25 = 154.25 2.25 + 3x + x2 = 154.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 154.25 Calculate the square root of the right side: 12.419742348 Break this problem into two subproblems by setting (x + 1.5) equal to 12.419742348 and -12.419742348.Subproblem 1
x + 1.5 = 12.419742348 Simplifying x + 1.5 = 12.419742348 Reorder the terms: 1.5 + x = 12.419742348 Solving 1.5 + x = 12.419742348 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 = 12.419742348 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 12.419742348 + -1.5 x = 12.419742348 + -1.5 Combine like terms: 12.419742348 + -1.5 = 10.919742348 x = 10.919742348 Simplifying x = 10.919742348Subproblem 2
x + 1.5 = -12.419742348 Simplifying x + 1.5 = -12.419742348 Reorder the terms: 1.5 + x = -12.419742348 Solving 1.5 + x = -12.419742348 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 = -12.419742348 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -12.419742348 + -1.5 x = -12.419742348 + -1.5 Combine like terms: -12.419742348 + -1.5 = -13.919742348 x = -13.919742348 Simplifying x = -13.919742348Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.919742348, -13.919742348}Solution
x = {10.919742348, -13.919742348}
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