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Simplifying x2 + 20x + -4200 = 0 Reorder the terms: -4200 + 20x + x2 = 0 Solving -4200 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4200' to each side of the equation. -4200 + 20x + 4200 + x2 = 0 + 4200 Reorder the terms: -4200 + 4200 + 20x + x2 = 0 + 4200 Combine like terms: -4200 + 4200 = 0 0 + 20x + x2 = 0 + 4200 20x + x2 = 0 + 4200 Combine like terms: 0 + 4200 = 4200 20x + x2 = 4200 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 = 4200 + 100 Reorder the terms: 100 + 20x + x2 = 4200 + 100 Combine like terms: 4200 + 100 = 4300 100 + 20x + x2 = 4300 Factor a perfect square on the left side: (x + 10)(x + 10) = 4300 Calculate the square root of the right side: 65.574385243 Break this problem into two subproblems by setting (x + 10) equal to 65.574385243 and -65.574385243.Subproblem 1
x + 10 = 65.574385243 Simplifying x + 10 = 65.574385243 Reorder the terms: 10 + x = 65.574385243 Solving 10 + x = 65.574385243 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 = 65.574385243 + -10 Combine like terms: 10 + -10 = 0 0 + x = 65.574385243 + -10 x = 65.574385243 + -10 Combine like terms: 65.574385243 + -10 = 55.574385243 x = 55.574385243 Simplifying x = 55.574385243Subproblem 2
x + 10 = -65.574385243 Simplifying x + 10 = -65.574385243 Reorder the terms: 10 + x = -65.574385243 Solving 10 + x = -65.574385243 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 = -65.574385243 + -10 Combine like terms: 10 + -10 = 0 0 + x = -65.574385243 + -10 x = -65.574385243 + -10 Combine like terms: -65.574385243 + -10 = -75.574385243 x = -75.574385243 Simplifying x = -75.574385243Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.574385243, -75.574385243}
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