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Simplifying 8x2 + 24x + 6 = 0 Reorder the terms: 6 + 24x + 8x2 = 0 Solving 6 + 24x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 12x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 12x + 4x2)' equal to zero and attempt to solve: Simplifying 3 + 12x + 4x2 = 0 Solving 3 + 12x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + 3x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 3x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 3x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 3x + x2 = 0 + -0.75 3x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 3x + x2 = -0.75 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -0.75 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -0.75 + 2.25 Combine like terms: -0.75 + 2.25 = 1.5 2.25 + 3x + x2 = 1.5 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + 1.5) equal to 1.224744871 and -1.224744871.Subproblem 1
x + 1.5 = 1.224744871 Simplifying x + 1.5 = 1.224744871 Reorder the terms: 1.5 + x = 1.224744871 Solving 1.5 + x = 1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.224744871 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.224744871 + -1.5 x = 1.224744871 + -1.5 Combine like terms: 1.224744871 + -1.5 = -0.275255129 x = -0.275255129 Simplifying x = -0.275255129Subproblem 2
x + 1.5 = -1.224744871 Simplifying x + 1.5 = -1.224744871 Reorder the terms: 1.5 + x = -1.224744871 Solving 1.5 + x = -1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.224744871 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.224744871 + -1.5 x = -1.224744871 + -1.5 Combine like terms: -1.224744871 + -1.5 = -2.724744871 x = -2.724744871 Simplifying x = -2.724744871Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.275255129, -2.724744871}Solution
x = {-0.275255129, -2.724744871}
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