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Simplifying 6x2 + 24x + 15 = 0 Reorder the terms: 15 + 24x + 6x2 = 0 Solving 15 + 24x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(5 + 8x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + 8x + 2x2)' equal to zero and attempt to solve: Simplifying 5 + 8x + 2x2 = 0 Solving 5 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 4x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 4x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 4x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 4x + x2 = 0 + -2.5 4x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 4x + x2 = -2.5 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -2.5 + 4 Reorder the terms: 4 + 4x + x2 = -2.5 + 4 Combine like terms: -2.5 + 4 = 1.5 4 + 4x + x2 = 1.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + 2) equal to 1.224744871 and -1.224744871.Subproblem 1
x + 2 = 1.224744871 Simplifying x + 2 = 1.224744871 Reorder the terms: 2 + x = 1.224744871 Solving 2 + x = 1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.224744871 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.224744871 + -2 x = 1.224744871 + -2 Combine like terms: 1.224744871 + -2 = -0.775255129 x = -0.775255129 Simplifying x = -0.775255129Subproblem 2
x + 2 = -1.224744871 Simplifying x + 2 = -1.224744871 Reorder the terms: 2 + x = -1.224744871 Solving 2 + x = -1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.224744871 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.224744871 + -2 x = -1.224744871 + -2 Combine like terms: -1.224744871 + -2 = -3.224744871 x = -3.224744871 Simplifying x = -3.224744871Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.775255129, -3.224744871}Solution
x = {-0.775255129, -3.224744871}
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