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Simplifying 3(x2 + 9x + -12) = 0 Reorder the terms: 3(-12 + 9x + x2) = 0 (-12 * 3 + 9x * 3 + x2 * 3) = 0 (-36 + 27x + 3x2) = 0 Solving -36 + 27x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-12 + 9x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-12 + 9x + x2)' equal to zero and attempt to solve: Simplifying -12 + 9x + x2 = 0 Solving -12 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 9x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 9x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 9x + x2 = 0 + 12 9x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 9x + x2 = 12 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 12 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 12 + 20.25 Combine like terms: 12 + 20.25 = 32.25 20.25 + 9x + x2 = 32.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (x + 4.5) equal to 5.678908346 and -5.678908346.Subproblem 1
x + 4.5 = 5.678908346 Simplifying x + 4.5 = 5.678908346 Reorder the terms: 4.5 + x = 5.678908346 Solving 4.5 + x = 5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 5.678908346 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 5.678908346 + -4.5 x = 5.678908346 + -4.5 Combine like terms: 5.678908346 + -4.5 = 1.178908346 x = 1.178908346 Simplifying x = 1.178908346Subproblem 2
x + 4.5 = -5.678908346 Simplifying x + 4.5 = -5.678908346 Reorder the terms: 4.5 + x = -5.678908346 Solving 4.5 + x = -5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -5.678908346 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -5.678908346 + -4.5 x = -5.678908346 + -4.5 Combine like terms: -5.678908346 + -4.5 = -10.178908346 x = -10.178908346 Simplifying x = -10.178908346Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.178908346, -10.178908346}Solution
x = {1.178908346, -10.178908346}
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