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Simplifying 6050 = x + x2 Solving 6050 = x + x2 Solving for variable 'x'. Reorder the terms: 6050 + -1x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 6050 + -1x + -1x2 = 0 + x2 + -1x2 6050 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 6050 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6050 + x + x2 = 0 Move the constant term to the right: Add '6050' to each side of the equation. -6050 + x + 6050 + x2 = 0 + 6050 Reorder the terms: -6050 + 6050 + x + x2 = 0 + 6050 Combine like terms: -6050 + 6050 = 0 0 + x + x2 = 0 + 6050 x + x2 = 0 + 6050 Combine like terms: 0 + 6050 = 6050 x + x2 = 6050 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 6050 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 6050 + 0.25 Combine like terms: 6050 + 0.25 = 6050.25 1.25 + x2 = 6050.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 6050.25 Calculate the square root of the right side: 77.783352975 Break this problem into two subproblems by setting (x + 0.5) equal to 77.783352975 and -77.783352975.Subproblem 1
x + 0.5 = 77.783352975 Simplifying x + 0.5 = 77.783352975 Reorder the terms: 0.5 + x = 77.783352975 Solving 0.5 + x = 77.783352975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 77.783352975 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 77.783352975 + -0.5 x = 77.783352975 + -0.5 Combine like terms: 77.783352975 + -0.5 = 77.283352975 x = 77.283352975 Simplifying x = 77.283352975Subproblem 2
x + 0.5 = -77.783352975 Simplifying x + 0.5 = -77.783352975 Reorder the terms: 0.5 + x = -77.783352975 Solving 0.5 + x = -77.783352975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -77.783352975 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -77.783352975 + -0.5 x = -77.783352975 + -0.5 Combine like terms: -77.783352975 + -0.5 = -78.283352975 x = -78.283352975 Simplifying x = -78.283352975Solution
The solution to the problem is based on the solutions from the subproblems. x = {77.283352975, -78.283352975}
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