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Simplifying 4x2 + 18x + -6 = 0 Reorder the terms: -6 + 18x + 4x2 = 0 Solving -6 + 18x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 9x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 9x + 2x2)' equal to zero and attempt to solve: Simplifying -3 + 9x + 2x2 = 0 Solving -3 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 4.5x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 4.5x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 4.5x + x2 = 0 + 1.5 4.5x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 4.5x + x2 = 1.5 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 1.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 1.5 + 5.0625 Combine like terms: 1.5 + 5.0625 = 6.5625 5.0625 + 4.5x + x2 = 6.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (x + 2.25) equal to 2.561737691 and -2.561737691.Subproblem 1
x + 2.25 = 2.561737691 Simplifying x + 2.25 = 2.561737691 Reorder the terms: 2.25 + x = 2.561737691 Solving 2.25 + x = 2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 2.561737691 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 2.561737691 + -2.25 x = 2.561737691 + -2.25 Combine like terms: 2.561737691 + -2.25 = 0.311737691 x = 0.311737691 Simplifying x = 0.311737691Subproblem 2
x + 2.25 = -2.561737691 Simplifying x + 2.25 = -2.561737691 Reorder the terms: 2.25 + x = -2.561737691 Solving 2.25 + x = -2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -2.561737691 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -2.561737691 + -2.25 x = -2.561737691 + -2.25 Combine like terms: -2.561737691 + -2.25 = -4.811737691 x = -4.811737691 Simplifying x = -4.811737691Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.311737691, -4.811737691}Solution
x = {0.311737691, -4.811737691}
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