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Simplifying 2x2 + 100x + -1000 = 0 Reorder the terms: -1000 + 100x + 2x2 = 0 Solving -1000 + 100x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-500 + 50x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-500 + 50x + x2)' equal to zero and attempt to solve: Simplifying -500 + 50x + x2 = 0 Solving -500 + 50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '500' to each side of the equation. -500 + 50x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + 50x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + 50x + x2 = 0 + 500 50x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 50x + x2 = 500 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = 500 + 625 Reorder the terms: 625 + 50x + x2 = 500 + 625 Combine like terms: 500 + 625 = 1125 625 + 50x + x2 = 1125 Factor a perfect square on the left side: (x + 25)(x + 25) = 1125 Calculate the square root of the right side: 33.541019662 Break this problem into two subproblems by setting (x + 25) equal to 33.541019662 and -33.541019662.Subproblem 1
x + 25 = 33.541019662 Simplifying x + 25 = 33.541019662 Reorder the terms: 25 + x = 33.541019662 Solving 25 + x = 33.541019662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 33.541019662 + -25 Combine like terms: 25 + -25 = 0 0 + x = 33.541019662 + -25 x = 33.541019662 + -25 Combine like terms: 33.541019662 + -25 = 8.541019662 x = 8.541019662 Simplifying x = 8.541019662Subproblem 2
x + 25 = -33.541019662 Simplifying x + 25 = -33.541019662 Reorder the terms: 25 + x = -33.541019662 Solving 25 + x = -33.541019662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -33.541019662 + -25 Combine like terms: 25 + -25 = 0 0 + x = -33.541019662 + -25 x = -33.541019662 + -25 Combine like terms: -33.541019662 + -25 = -58.541019662 x = -58.541019662 Simplifying x = -58.541019662Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.541019662, -58.541019662}Solution
x = {8.541019662, -58.541019662}
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