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Simplifying 2x2 + 40x = 8002 Reorder the terms: 40x + 2x2 = 8002 Solving 40x + 2x2 = 8002 Solving for variable 'x'. Reorder the terms: -8002 + 40x + 2x2 = 8002 + -8002 Combine like terms: 8002 + -8002 = 0 -8002 + 40x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4001 + 20x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4001 + 20x + x2)' equal to zero and attempt to solve: Simplifying -4001 + 20x + x2 = 0 Solving -4001 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4001' to each side of the equation. -4001 + 20x + 4001 + x2 = 0 + 4001 Reorder the terms: -4001 + 4001 + 20x + x2 = 0 + 4001 Combine like terms: -4001 + 4001 = 0 0 + 20x + x2 = 0 + 4001 20x + x2 = 0 + 4001 Combine like terms: 0 + 4001 = 4001 20x + x2 = 4001 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 4001 + 100 Reorder the terms: 100 + 20x + x2 = 4001 + 100 Combine like terms: 4001 + 100 = 4101 100 + 20x + x2 = 4101 Factor a perfect square on the left side: (x + 10)(x + 10) = 4101 Calculate the square root of the right side: 64.039050586 Break this problem into two subproblems by setting (x + 10) equal to 64.039050586 and -64.039050586.Subproblem 1
x + 10 = 64.039050586 Simplifying x + 10 = 64.039050586 Reorder the terms: 10 + x = 64.039050586 Solving 10 + x = 64.039050586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 64.039050586 + -10 Combine like terms: 10 + -10 = 0 0 + x = 64.039050586 + -10 x = 64.039050586 + -10 Combine like terms: 64.039050586 + -10 = 54.039050586 x = 54.039050586 Simplifying x = 54.039050586Subproblem 2
x + 10 = -64.039050586 Simplifying x + 10 = -64.039050586 Reorder the terms: 10 + x = -64.039050586 Solving 10 + x = -64.039050586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -64.039050586 + -10 Combine like terms: 10 + -10 = 0 0 + x = -64.039050586 + -10 x = -64.039050586 + -10 Combine like terms: -64.039050586 + -10 = -74.039050586 x = -74.039050586 Simplifying x = -74.039050586Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.039050586, -74.039050586}Solution
x = {54.039050586, -74.039050586}
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