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Simplifying -2x2 + 1200x + 4000 = 0 Reorder the terms: 4000 + 1200x + -2x2 = 0 Solving 4000 + 1200x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2000 + 600x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2000 + 600x + -1x2)' equal to zero and attempt to solve: Simplifying 2000 + 600x + -1x2 = 0 Solving 2000 + 600x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2000 + -600x + x2 = 0 Move the constant term to the right: Add '2000' to each side of the equation. -2000 + -600x + 2000 + x2 = 0 + 2000 Reorder the terms: -2000 + 2000 + -600x + x2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + -600x + x2 = 0 + 2000 -600x + x2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 -600x + x2 = 2000 The x term is -600x. Take half its coefficient (-300). Square it (90000) and add it to both sides. Add '90000' to each side of the equation. -600x + 90000 + x2 = 2000 + 90000 Reorder the terms: 90000 + -600x + x2 = 2000 + 90000 Combine like terms: 2000 + 90000 = 92000 90000 + -600x + x2 = 92000 Factor a perfect square on the left side: (x + -300)(x + -300) = 92000 Calculate the square root of the right side: 303.315017762 Break this problem into two subproblems by setting (x + -300) equal to 303.315017762 and -303.315017762.Subproblem 1
x + -300 = 303.315017762 Simplifying x + -300 = 303.315017762 Reorder the terms: -300 + x = 303.315017762 Solving -300 + x = 303.315017762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + x = 303.315017762 + 300 Combine like terms: -300 + 300 = 0 0 + x = 303.315017762 + 300 x = 303.315017762 + 300 Combine like terms: 303.315017762 + 300 = 603.315017762 x = 603.315017762 Simplifying x = 603.315017762Subproblem 2
x + -300 = -303.315017762 Simplifying x + -300 = -303.315017762 Reorder the terms: -300 + x = -303.315017762 Solving -300 + x = -303.315017762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + x = -303.315017762 + 300 Combine like terms: -300 + 300 = 0 0 + x = -303.315017762 + 300 x = -303.315017762 + 300 Combine like terms: -303.315017762 + 300 = -3.315017762 x = -3.315017762 Simplifying x = -3.315017762Solution
The solution to the problem is based on the solutions from the subproblems. x = {603.315017762, -3.315017762}Solution
x = {603.315017762, -3.315017762}
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