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Simplifying 2x2 + 80x + 2000 = 22400 Reorder the terms: 2000 + 80x + 2x2 = 22400 Solving 2000 + 80x + 2x2 = 22400 Solving for variable 'x'. Reorder the terms: 2000 + -22400 + 80x + 2x2 = 22400 + -22400 Combine like terms: 2000 + -22400 = -20400 -20400 + 80x + 2x2 = 22400 + -22400 Combine like terms: 22400 + -22400 = 0 -20400 + 80x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10200 + 40x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10200 + 40x + x2)' equal to zero and attempt to solve: Simplifying -10200 + 40x + x2 = 0 Solving -10200 + 40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10200' to each side of the equation. -10200 + 40x + 10200 + x2 = 0 + 10200 Reorder the terms: -10200 + 10200 + 40x + x2 = 0 + 10200 Combine like terms: -10200 + 10200 = 0 0 + 40x + x2 = 0 + 10200 40x + x2 = 0 + 10200 Combine like terms: 0 + 10200 = 10200 40x + x2 = 10200 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 = 10200 + 400 Reorder the terms: 400 + 40x + x2 = 10200 + 400 Combine like terms: 10200 + 400 = 10600 400 + 40x + x2 = 10600 Factor a perfect square on the left side: (x + 20)(x + 20) = 10600 Calculate the square root of the right side: 102.95630141 Break this problem into two subproblems by setting (x + 20) equal to 102.95630141 and -102.95630141.Subproblem 1
x + 20 = 102.95630141 Simplifying x + 20 = 102.95630141 Reorder the terms: 20 + x = 102.95630141 Solving 20 + x = 102.95630141 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 = 102.95630141 + -20 Combine like terms: 20 + -20 = 0 0 + x = 102.95630141 + -20 x = 102.95630141 + -20 Combine like terms: 102.95630141 + -20 = 82.95630141 x = 82.95630141 Simplifying x = 82.95630141Subproblem 2
x + 20 = -102.95630141 Simplifying x + 20 = -102.95630141 Reorder the terms: 20 + x = -102.95630141 Solving 20 + x = -102.95630141 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 = -102.95630141 + -20 Combine like terms: 20 + -20 = 0 0 + x = -102.95630141 + -20 x = -102.95630141 + -20 Combine like terms: -102.95630141 + -20 = -122.95630141 x = -122.95630141 Simplifying x = -122.95630141Solution
The solution to the problem is based on the solutions from the subproblems. x = {82.95630141, -122.95630141}Solution
x = {82.95630141, -122.95630141}
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