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Simplifying 4x2 + 24x + 30 = 0 Reorder the terms: 30 + 24x + 4x2 = 0 Solving 30 + 24x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 12x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + 12x + 2x2)' equal to zero and attempt to solve: Simplifying 15 + 12x + 2x2 = 0 Solving 15 + 12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + 6x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 6x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 6x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 6x + x2 = 0 + -7.5 6x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 6x + x2 = -7.5 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -7.5 + 9 Reorder the terms: 9 + 6x + x2 = -7.5 + 9 Combine like terms: -7.5 + 9 = 1.5 9 + 6x + x2 = 1.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + 3) equal to 1.224744871 and -1.224744871.Subproblem 1
x + 3 = 1.224744871 Simplifying x + 3 = 1.224744871 Reorder the terms: 3 + x = 1.224744871 Solving 3 + x = 1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 1.224744871 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.224744871 + -3 x = 1.224744871 + -3 Combine like terms: 1.224744871 + -3 = -1.775255129 x = -1.775255129 Simplifying x = -1.775255129Subproblem 2
x + 3 = -1.224744871 Simplifying x + 3 = -1.224744871 Reorder the terms: 3 + x = -1.224744871 Solving 3 + x = -1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -1.224744871 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.224744871 + -3 x = -1.224744871 + -3 Combine like terms: -1.224744871 + -3 = -4.224744871 x = -4.224744871 Simplifying x = -4.224744871Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.775255129, -4.224744871}Solution
x = {-1.775255129, -4.224744871}
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