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Simplifying (5x + -8)(14x + -18) = 24 * 24 Reorder the terms: (-8 + 5x)(14x + -18) = 24 * 24 Reorder the terms: (-8 + 5x)(-18 + 14x) = 24 * 24 Multiply (-8 + 5x) * (-18 + 14x) (-8(-18 + 14x) + 5x * (-18 + 14x)) = 24 * 24 ((-18 * -8 + 14x * -8) + 5x * (-18 + 14x)) = 24 * 24 ((144 + -112x) + 5x * (-18 + 14x)) = 24 * 24 (144 + -112x + (-18 * 5x + 14x * 5x)) = 24 * 24 (144 + -112x + (-90x + 70x2)) = 24 * 24 Combine like terms: -112x + -90x = -202x (144 + -202x + 70x2) = 24 * 24 Multiply 24 * 24 144 + -202x + 70x2 = 576 Solving 144 + -202x + 70x2 = 576 Solving for variable 'x'. Reorder the terms: 144 + -576 + -202x + 70x2 = 576 + -576 Combine like terms: 144 + -576 = -432 -432 + -202x + 70x2 = 576 + -576 Combine like terms: 576 + -576 = 0 -432 + -202x + 70x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-216 + -101x + 35x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-216 + -101x + 35x2)' equal to zero and attempt to solve: Simplifying -216 + -101x + 35x2 = 0 Solving -216 + -101x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -6.171428571 + -2.885714286x + x2 = 0 Move the constant term to the right: Add '6.171428571' to each side of the equation. -6.171428571 + -2.885714286x + 6.171428571 + x2 = 0 + 6.171428571 Reorder the terms: -6.171428571 + 6.171428571 + -2.885714286x + x2 = 0 + 6.171428571 Combine like terms: -6.171428571 + 6.171428571 = 0.000000000 0.000000000 + -2.885714286x + x2 = 0 + 6.171428571 -2.885714286x + x2 = 0 + 6.171428571 Combine like terms: 0 + 6.171428571 = 6.171428571 -2.885714286x + x2 = 6.171428571 The x term is -2.885714286x. Take half its coefficient (-1.442857143). Square it (2.081836735) and add it to both sides. Add '2.081836735' to each side of the equation. -2.885714286x + 2.081836735 + x2 = 6.171428571 + 2.081836735 Reorder the terms: 2.081836735 + -2.885714286x + x2 = 6.171428571 + 2.081836735 Combine like terms: 6.171428571 + 2.081836735 = 8.253265306 2.081836735 + -2.885714286x + x2 = 8.253265306 Factor a perfect square on the left side: (x + -1.442857143)(x + -1.442857143) = 8.253265306 Calculate the square root of the right side: 2.872849684 Break this problem into two subproblems by setting (x + -1.442857143) equal to 2.872849684 and -2.872849684.Subproblem 1
x + -1.442857143 = 2.872849684 Simplifying x + -1.442857143 = 2.872849684 Reorder the terms: -1.442857143 + x = 2.872849684 Solving -1.442857143 + x = 2.872849684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.442857143' to each side of the equation. -1.442857143 + 1.442857143 + x = 2.872849684 + 1.442857143 Combine like terms: -1.442857143 + 1.442857143 = 0.000000000 0.000000000 + x = 2.872849684 + 1.442857143 x = 2.872849684 + 1.442857143 Combine like terms: 2.872849684 + 1.442857143 = 4.315706827 x = 4.315706827 Simplifying x = 4.315706827Subproblem 2
x + -1.442857143 = -2.872849684 Simplifying x + -1.442857143 = -2.872849684 Reorder the terms: -1.442857143 + x = -2.872849684 Solving -1.442857143 + x = -2.872849684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.442857143' to each side of the equation. -1.442857143 + 1.442857143 + x = -2.872849684 + 1.442857143 Combine like terms: -1.442857143 + 1.442857143 = 0.000000000 0.000000000 + x = -2.872849684 + 1.442857143 x = -2.872849684 + 1.442857143 Combine like terms: -2.872849684 + 1.442857143 = -1.429992541 x = -1.429992541 Simplifying x = -1.429992541Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.315706827, -1.429992541}Solution
x = {4.315706827, -1.429992541}
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