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Simplifying 6x2 + 48x + 6 = 0 Reorder the terms: 6 + 48x + 6x2 = 0 Solving 6 + 48x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(1 + 8x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(1 + 8x + x2)' equal to zero and attempt to solve: Simplifying 1 + 8x + x2 = 0 Solving 1 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 8x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 8x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8x + x2 = 0 + -1 8x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 8x + x2 = -1 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 = -1 + 16 Reorder the terms: 16 + 8x + x2 = -1 + 16 Combine like terms: -1 + 16 = 15 16 + 8x + x2 = 15 Factor a perfect square on the left side: (x + 4)(x + 4) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + 4) equal to 3.872983346 and -3.872983346.Subproblem 1
x + 4 = 3.872983346 Simplifying x + 4 = 3.872983346 Reorder the terms: 4 + x = 3.872983346 Solving 4 + x = 3.872983346 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 = 3.872983346 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.872983346 + -4 x = 3.872983346 + -4 Combine like terms: 3.872983346 + -4 = -0.127016654 x = -0.127016654 Simplifying x = -0.127016654Subproblem 2
x + 4 = -3.872983346 Simplifying x + 4 = -3.872983346 Reorder the terms: 4 + x = -3.872983346 Solving 4 + x = -3.872983346 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 = -3.872983346 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.872983346 + -4 x = -3.872983346 + -4 Combine like terms: -3.872983346 + -4 = -7.872983346 x = -7.872983346 Simplifying x = -7.872983346Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.127016654, -7.872983346}Solution
x = {-0.127016654, -7.872983346}
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