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Simplifying (2x + 16)(3x + -10) = 44 Reorder the terms: (16 + 2x)(3x + -10) = 44 Reorder the terms: (16 + 2x)(-10 + 3x) = 44 Multiply (16 + 2x) * (-10 + 3x) (16(-10 + 3x) + 2x * (-10 + 3x)) = 44 ((-10 * 16 + 3x * 16) + 2x * (-10 + 3x)) = 44 ((-160 + 48x) + 2x * (-10 + 3x)) = 44 (-160 + 48x + (-10 * 2x + 3x * 2x)) = 44 (-160 + 48x + (-20x + 6x2)) = 44 Combine like terms: 48x + -20x = 28x (-160 + 28x + 6x2) = 44 Solving -160 + 28x + 6x2 = 44 Solving for variable 'x'. Reorder the terms: -160 + -44 + 28x + 6x2 = 44 + -44 Combine like terms: -160 + -44 = -204 -204 + 28x + 6x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -204 + 28x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-102 + 14x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-102 + 14x + 3x2)' equal to zero and attempt to solve: Simplifying -102 + 14x + 3x2 = 0 Solving -102 + 14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -34 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '34' to each side of the equation. -34 + 4.666666667x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + 4.666666667x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 4.666666667x + x2 = 0 + 34 4.666666667x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 4.666666667x + x2 = 34 The x term is 4.666666667x. Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. 4.666666667x + 5.444444448 + x2 = 34 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = 34 + 5.444444448 Combine like terms: 34 + 5.444444448 = 39.444444448 5.444444448 + 4.666666667x + x2 = 39.444444448 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = 39.444444448 Calculate the square root of the right side: 6.280481227 Break this problem into two subproblems by setting (x + 2.333333334) equal to 6.280481227 and -6.280481227.Subproblem 1
x + 2.333333334 = 6.280481227 Simplifying x + 2.333333334 = 6.280481227 Reorder the terms: 2.333333334 + x = 6.280481227 Solving 2.333333334 + x = 6.280481227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = 6.280481227 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 6.280481227 + -2.333333334 x = 6.280481227 + -2.333333334 Combine like terms: 6.280481227 + -2.333333334 = 3.947147893 x = 3.947147893 Simplifying x = 3.947147893Subproblem 2
x + 2.333333334 = -6.280481227 Simplifying x + 2.333333334 = -6.280481227 Reorder the terms: 2.333333334 + x = -6.280481227 Solving 2.333333334 + x = -6.280481227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = -6.280481227 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -6.280481227 + -2.333333334 x = -6.280481227 + -2.333333334 Combine like terms: -6.280481227 + -2.333333334 = -8.613814561 x = -8.613814561 Simplifying x = -8.613814561Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.947147893, -8.613814561}Solution
x = {3.947147893, -8.613814561}
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