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Simplifying 0 = 3x2 + 24x + 44 Reorder the terms: 0 = 44 + 24x + 3x2 Solving 0 = 44 + 24x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -44 = -44 -44 + -24x + -3x2 = 44 + 24x + 3x2 + -44 + -24x + -3x2 Reorder the terms: -44 + -24x + -3x2 = 44 + -44 + 24x + -24x + 3x2 + -3x2 Combine like terms: 44 + -44 = 0 -44 + -24x + -3x2 = 0 + 24x + -24x + 3x2 + -3x2 -44 + -24x + -3x2 = 24x + -24x + 3x2 + -3x2 Combine like terms: 24x + -24x = 0 -44 + -24x + -3x2 = 0 + 3x2 + -3x2 -44 + -24x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -44 + -24x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(44 + 24x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(44 + 24x + 3x2)' equal to zero and attempt to solve: Simplifying 44 + 24x + 3x2 = 0 Solving 44 + 24x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 14.66666667 + 8x + x2 = 0 Move the constant term to the right: Add '-14.66666667' to each side of the equation. 14.66666667 + 8x + -14.66666667 + x2 = 0 + -14.66666667 Reorder the terms: 14.66666667 + -14.66666667 + 8x + x2 = 0 + -14.66666667 Combine like terms: 14.66666667 + -14.66666667 = 0.00000000 0.00000000 + 8x + x2 = 0 + -14.66666667 8x + x2 = 0 + -14.66666667 Combine like terms: 0 + -14.66666667 = -14.66666667 8x + x2 = -14.66666667 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 = -14.66666667 + 16 Reorder the terms: 16 + 8x + x2 = -14.66666667 + 16 Combine like terms: -14.66666667 + 16 = 1.33333333 16 + 8x + x2 = 1.33333333 Factor a perfect square on the left side: (x + 4)(x + 4) = 1.33333333 Calculate the square root of the right side: 1.154700537 Break this problem into two subproblems by setting (x + 4) equal to 1.154700537 and -1.154700537.Subproblem 1
x + 4 = 1.154700537 Simplifying x + 4 = 1.154700537 Reorder the terms: 4 + x = 1.154700537 Solving 4 + x = 1.154700537 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 = 1.154700537 + -4 Combine like terms: 4 + -4 = 0 0 + x = 1.154700537 + -4 x = 1.154700537 + -4 Combine like terms: 1.154700537 + -4 = -2.845299463 x = -2.845299463 Simplifying x = -2.845299463Subproblem 2
x + 4 = -1.154700537 Simplifying x + 4 = -1.154700537 Reorder the terms: 4 + x = -1.154700537 Solving 4 + x = -1.154700537 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 = -1.154700537 + -4 Combine like terms: 4 + -4 = 0 0 + x = -1.154700537 + -4 x = -1.154700537 + -4 Combine like terms: -1.154700537 + -4 = -5.154700537 x = -5.154700537 Simplifying x = -5.154700537Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.845299463, -5.154700537}Solution
x = {-2.845299463, -5.154700537}
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