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Simplifying -10x2 + -100x = 44 Reorder the terms: -100x + -10x2 = 44 Solving -100x + -10x2 = 44 Solving for variable 'x'. Reorder the terms: -44 + -100x + -10x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + -100x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(22 + 50x + 5x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(22 + 50x + 5x2)' equal to zero and attempt to solve: Simplifying 22 + 50x + 5x2 = 0 Solving 22 + 50x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4.4 + 10x + x2 = 0 Move the constant term to the right: Add '-4.4' to each side of the equation. 4.4 + 10x + -4.4 + x2 = 0 + -4.4 Reorder the terms: 4.4 + -4.4 + 10x + x2 = 0 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + 10x + x2 = 0 + -4.4 10x + x2 = 0 + -4.4 Combine like terms: 0 + -4.4 = -4.4 10x + x2 = -4.4 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -4.4 + 25 Reorder the terms: 25 + 10x + x2 = -4.4 + 25 Combine like terms: -4.4 + 25 = 20.6 25 + 10x + x2 = 20.6 Factor a perfect square on the left side: (x + 5)(x + 5) = 20.6 Calculate the square root of the right side: 4.538722287 Break this problem into two subproblems by setting (x + 5) equal to 4.538722287 and -4.538722287.Subproblem 1
x + 5 = 4.538722287 Simplifying x + 5 = 4.538722287 Reorder the terms: 5 + x = 4.538722287 Solving 5 + x = 4.538722287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 4.538722287 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.538722287 + -5 x = 4.538722287 + -5 Combine like terms: 4.538722287 + -5 = -0.461277713 x = -0.461277713 Simplifying x = -0.461277713Subproblem 2
x + 5 = -4.538722287 Simplifying x + 5 = -4.538722287 Reorder the terms: 5 + x = -4.538722287 Solving 5 + x = -4.538722287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -4.538722287 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.538722287 + -5 x = -4.538722287 + -5 Combine like terms: -4.538722287 + -5 = -9.538722287 x = -9.538722287 Simplifying x = -9.538722287Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.461277713, -9.538722287}Solution
x = {-0.461277713, -9.538722287}
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