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Simplifying 0 = 3x2 + 12x + 8 Reorder the terms: 0 = 8 + 12x + 3x2 Solving 0 = 8 + 12x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -8 = -8 -8 + -12x + -3x2 = 8 + 12x + 3x2 + -8 + -12x + -3x2 Reorder the terms: -8 + -12x + -3x2 = 8 + -8 + 12x + -12x + 3x2 + -3x2 Combine like terms: 8 + -8 = 0 -8 + -12x + -3x2 = 0 + 12x + -12x + 3x2 + -3x2 -8 + -12x + -3x2 = 12x + -12x + 3x2 + -3x2 Combine like terms: 12x + -12x = 0 -8 + -12x + -3x2 = 0 + 3x2 + -3x2 -8 + -12x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -8 + -12x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 12x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 12x + 3x2)' equal to zero and attempt to solve: Simplifying 8 + 12x + 3x2 = 0 Solving 8 + 12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.666666667 + 4x + x2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + 4x + -2.666666667 + x2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + 4x + x2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + 4x + x2 = 0 + -2.666666667 4x + x2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 4x + x2 = -2.666666667 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 = -2.666666667 + 4 Reorder the terms: 4 + 4x + x2 = -2.666666667 + 4 Combine like terms: -2.666666667 + 4 = 1.333333333 4 + 4x + x2 = 1.333333333 Factor a perfect square on the left side: (x + 2)(x + 2) = 1.333333333 Calculate the square root of the right side: 1.154700538 Break this problem into two subproblems by setting (x + 2) equal to 1.154700538 and -1.154700538.Subproblem 1
x + 2 = 1.154700538 Simplifying x + 2 = 1.154700538 Reorder the terms: 2 + x = 1.154700538 Solving 2 + x = 1.154700538 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 = 1.154700538 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.154700538 + -2 x = 1.154700538 + -2 Combine like terms: 1.154700538 + -2 = -0.845299462 x = -0.845299462 Simplifying x = -0.845299462Subproblem 2
x + 2 = -1.154700538 Simplifying x + 2 = -1.154700538 Reorder the terms: 2 + x = -1.154700538 Solving 2 + x = -1.154700538 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 = -1.154700538 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.154700538 + -2 x = -1.154700538 + -2 Combine like terms: -1.154700538 + -2 = -3.154700538 x = -3.154700538 Simplifying x = -3.154700538Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.845299462, -3.154700538}Solution
x = {-0.845299462, -3.154700538}
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