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Simplifying 2x2 + 18x + -12 = 0 Reorder the terms: -12 + 18x + 2x2 = 0 Solving -12 + 18x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 9x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 9x + x2)' equal to zero and attempt to solve: Simplifying -6 + 9x + x2 = 0 Solving -6 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 9x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 9x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 9x + x2 = 0 + 6 9x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 9x + x2 = 6 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 = 6 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 6 + 20.25 Combine like terms: 6 + 20.25 = 26.25 20.25 + 9x + x2 = 26.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (x + 4.5) equal to 5.123475383 and -5.123475383.Subproblem 1
x + 4.5 = 5.123475383 Simplifying x + 4.5 = 5.123475383 Reorder the terms: 4.5 + x = 5.123475383 Solving 4.5 + x = 5.123475383 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 = 5.123475383 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 5.123475383 + -4.5 x = 5.123475383 + -4.5 Combine like terms: 5.123475383 + -4.5 = 0.623475383 x = 0.623475383 Simplifying x = 0.623475383Subproblem 2
x + 4.5 = -5.123475383 Simplifying x + 4.5 = -5.123475383 Reorder the terms: 4.5 + x = -5.123475383 Solving 4.5 + x = -5.123475383 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 = -5.123475383 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -5.123475383 + -4.5 x = -5.123475383 + -4.5 Combine like terms: -5.123475383 + -4.5 = -9.623475383 x = -9.623475383 Simplifying x = -9.623475383Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.623475383, -9.623475383}Solution
x = {0.623475383, -9.623475383}
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