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Simplifying (10 + -1x)(200 + 4x) = 224 Multiply (10 + -1x) * (200 + 4x) (10(200 + 4x) + -1x * (200 + 4x)) = 224 ((200 * 10 + 4x * 10) + -1x * (200 + 4x)) = 224 ((2000 + 40x) + -1x * (200 + 4x)) = 224 (2000 + 40x + (200 * -1x + 4x * -1x)) = 224 (2000 + 40x + (-200x + -4x2)) = 224 Combine like terms: 40x + -200x = -160x (2000 + -160x + -4x2) = 224 Solving 2000 + -160x + -4x2 = 224 Solving for variable 'x'. Reorder the terms: 2000 + -224 + -160x + -4x2 = 224 + -224 Combine like terms: 2000 + -224 = 1776 1776 + -160x + -4x2 = 224 + -224 Combine like terms: 224 + -224 = 0 1776 + -160x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(444 + -40x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(444 + -40x + -1x2)' equal to zero and attempt to solve: Simplifying 444 + -40x + -1x2 = 0 Solving 444 + -40x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -444 + 40x + x2 = 0 Move the constant term to the right: Add '444' to each side of the equation. -444 + 40x + 444 + x2 = 0 + 444 Reorder the terms: -444 + 444 + 40x + x2 = 0 + 444 Combine like terms: -444 + 444 = 0 0 + 40x + x2 = 0 + 444 40x + x2 = 0 + 444 Combine like terms: 0 + 444 = 444 40x + x2 = 444 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = 444 + 400 Reorder the terms: 400 + 40x + x2 = 444 + 400 Combine like terms: 444 + 400 = 844 400 + 40x + x2 = 844 Factor a perfect square on the left side: (x + 20)(x + 20) = 844 Calculate the square root of the right side: 29.051678093 Break this problem into two subproblems by setting (x + 20) equal to 29.051678093 and -29.051678093.Subproblem 1
x + 20 = 29.051678093 Simplifying x + 20 = 29.051678093 Reorder the terms: 20 + x = 29.051678093 Solving 20 + x = 29.051678093 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 29.051678093 + -20 Combine like terms: 20 + -20 = 0 0 + x = 29.051678093 + -20 x = 29.051678093 + -20 Combine like terms: 29.051678093 + -20 = 9.051678093 x = 9.051678093 Simplifying x = 9.051678093Subproblem 2
x + 20 = -29.051678093 Simplifying x + 20 = -29.051678093 Reorder the terms: 20 + x = -29.051678093 Solving 20 + x = -29.051678093 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -29.051678093 + -20 Combine like terms: 20 + -20 = 0 0 + x = -29.051678093 + -20 x = -29.051678093 + -20 Combine like terms: -29.051678093 + -20 = -49.051678093 x = -49.051678093 Simplifying x = -49.051678093Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.051678093, -49.051678093}Solution
x = {9.051678093, -49.051678093}
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