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Simplifying 4x2 + 24x + 10 = 0 Reorder the terms: 10 + 24x + 4x2 = 0 Solving 10 + 24x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 12x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 12x + 2x2)' equal to zero and attempt to solve: Simplifying 5 + 12x + 2x2 = 0 Solving 5 + 12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 6x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 6x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 6x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 6x + x2 = 0 + -2.5 6x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 6x + x2 = -2.5 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 = -2.5 + 9 Reorder the terms: 9 + 6x + x2 = -2.5 + 9 Combine like terms: -2.5 + 9 = 6.5 9 + 6x + x2 = 6.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (x + 3) equal to 2.549509757 and -2.549509757.Subproblem 1
x + 3 = 2.549509757 Simplifying x + 3 = 2.549509757 Reorder the terms: 3 + x = 2.549509757 Solving 3 + x = 2.549509757 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 = 2.549509757 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.549509757 + -3 x = 2.549509757 + -3 Combine like terms: 2.549509757 + -3 = -0.450490243 x = -0.450490243 Simplifying x = -0.450490243Subproblem 2
x + 3 = -2.549509757 Simplifying x + 3 = -2.549509757 Reorder the terms: 3 + x = -2.549509757 Solving 3 + x = -2.549509757 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 = -2.549509757 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.549509757 + -3 x = -2.549509757 + -3 Combine like terms: -2.549509757 + -3 = -5.549509757 x = -5.549509757 Simplifying x = -5.549509757Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.450490243, -5.549509757}Solution
x = {-0.450490243, -5.549509757}
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