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Simplifying 2x2 + 18x + 24 = 0 Reorder the terms: 24 + 18x + 2x2 = 0 Solving 24 + 18x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 9x + x2) = 0 Ignore the factor 2.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 = 8.25 20.25 + 9x + x2 = 8.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x + 4.5) equal to 2.872281323 and -2.872281323.Subproblem 1
x + 4.5 = 2.872281323 Simplifying x + 4.5 = 2.872281323 Reorder the terms: 4.5 + x = 2.872281323 Solving 4.5 + x = 2.872281323 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 = 2.872281323 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 2.872281323 + -4.5 x = 2.872281323 + -4.5 Combine like terms: 2.872281323 + -4.5 = -1.627718677 x = -1.627718677 Simplifying x = -1.627718677Subproblem 2
x + 4.5 = -2.872281323 Simplifying x + 4.5 = -2.872281323 Reorder the terms: 4.5 + x = -2.872281323 Solving 4.5 + x = -2.872281323 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 = -2.872281323 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -2.872281323 + -4.5 x = -2.872281323 + -4.5 Combine like terms: -2.872281323 + -4.5 = -7.372281323 x = -7.372281323 Simplifying x = -7.372281323Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.627718677, -7.372281323}Solution
x = {-1.627718677, -7.372281323}
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