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Simplifying 0 = 6x2 + 48x + 10 Reorder the terms: 0 = 10 + 48x + 6x2 Solving 0 = 10 + 48x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -10 = -10 -10 + -48x + -6x2 = 10 + 48x + 6x2 + -10 + -48x + -6x2 Reorder the terms: -10 + -48x + -6x2 = 10 + -10 + 48x + -48x + 6x2 + -6x2 Combine like terms: 10 + -10 = 0 -10 + -48x + -6x2 = 0 + 48x + -48x + 6x2 + -6x2 -10 + -48x + -6x2 = 48x + -48x + 6x2 + -6x2 Combine like terms: 48x + -48x = 0 -10 + -48x + -6x2 = 0 + 6x2 + -6x2 -10 + -48x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -10 + -48x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(5 + 24x + 3x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(5 + 24x + 3x2)' equal to zero and attempt to solve: Simplifying 5 + 24x + 3x2 = 0 Solving 5 + 24x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + 8x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + 8x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + 8x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + 8x + x2 = 0 + -1.666666667 8x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 8x + x2 = -1.666666667 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 = -1.666666667 + 16 Reorder the terms: 16 + 8x + x2 = -1.666666667 + 16 Combine like terms: -1.666666667 + 16 = 14.333333333 16 + 8x + x2 = 14.333333333 Factor a perfect square on the left side: (x + 4)(x + 4) = 14.333333333 Calculate the square root of the right side: 3.785938897 Break this problem into two subproblems by setting (x + 4) equal to 3.785938897 and -3.785938897.Subproblem 1
x + 4 = 3.785938897 Simplifying x + 4 = 3.785938897 Reorder the terms: 4 + x = 3.785938897 Solving 4 + x = 3.785938897 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 = 3.785938897 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.785938897 + -4 x = 3.785938897 + -4 Combine like terms: 3.785938897 + -4 = -0.214061103 x = -0.214061103 Simplifying x = -0.214061103Subproblem 2
x + 4 = -3.785938897 Simplifying x + 4 = -3.785938897 Reorder the terms: 4 + x = -3.785938897 Solving 4 + x = -3.785938897 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 = -3.785938897 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.785938897 + -4 x = -3.785938897 + -4 Combine like terms: -3.785938897 + -4 = -7.785938897 x = -7.785938897 Simplifying x = -7.785938897Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.214061103, -7.785938897}Solution
x = {-0.214061103, -7.785938897}
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