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Simplifying 6x2 + 48x + 18 = 0 Reorder the terms: 18 + 48x + 6x2 = 0 Solving 18 + 48x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(3 + 8x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(3 + 8x + x2)' equal to zero and attempt to solve: Simplifying 3 + 8x + x2 = 0 Solving 3 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 8x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 8x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 8x + x2 = 0 + -3 8x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 8x + x2 = -3 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -3 + 16 Reorder the terms: 16 + 8x + x2 = -3 + 16 Combine like terms: -3 + 16 = 13 16 + 8x + x2 = 13 Factor a perfect square on the left side: (x + 4)(x + 4) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + 4) equal to 3.605551275 and -3.605551275.Subproblem 1
x + 4 = 3.605551275 Simplifying x + 4 = 3.605551275 Reorder the terms: 4 + x = 3.605551275 Solving 4 + x = 3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 3.605551275 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.605551275 + -4 x = 3.605551275 + -4 Combine like terms: 3.605551275 + -4 = -0.394448725 x = -0.394448725 Simplifying x = -0.394448725Subproblem 2
x + 4 = -3.605551275 Simplifying x + 4 = -3.605551275 Reorder the terms: 4 + x = -3.605551275 Solving 4 + x = -3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -3.605551275 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.605551275 + -4 x = -3.605551275 + -4 Combine like terms: -3.605551275 + -4 = -7.605551275 x = -7.605551275 Simplifying x = -7.605551275Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.394448725, -7.605551275}Solution
x = {-0.394448725, -7.605551275}
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