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Simplifying 0.5x2 + 300x + -4600 = 0 Reorder the terms: -4600 + 300x + 0.5x2 = 0 Solving -4600 + 300x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -9200 + 600x + x2 = 0 Move the constant term to the right: Add '9200' to each side of the equation. -9200 + 600x + 9200 + x2 = 0 + 9200 Reorder the terms: -9200 + 9200 + 600x + x2 = 0 + 9200 Combine like terms: -9200 + 9200 = 0 0 + 600x + x2 = 0 + 9200 600x + x2 = 0 + 9200 Combine like terms: 0 + 9200 = 9200 600x + x2 = 9200 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 = 9200 + 90000 Reorder the terms: 90000 + 600x + x2 = 9200 + 90000 Combine like terms: 9200 + 90000 = 99200 90000 + 600x + x2 = 99200 Factor a perfect square on the left side: (x + 300)(x + 300) = 99200 Calculate the square root of the right side: 314.96031496 Break this problem into two subproblems by setting (x + 300) equal to 314.96031496 and -314.96031496.Subproblem 1
x + 300 = 314.96031496 Simplifying x + 300 = 314.96031496 Reorder the terms: 300 + x = 314.96031496 Solving 300 + x = 314.96031496 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 = 314.96031496 + -300 Combine like terms: 300 + -300 = 0 0 + x = 314.96031496 + -300 x = 314.96031496 + -300 Combine like terms: 314.96031496 + -300 = 14.96031496 x = 14.96031496 Simplifying x = 14.96031496Subproblem 2
x + 300 = -314.96031496 Simplifying x + 300 = -314.96031496 Reorder the terms: 300 + x = -314.96031496 Solving 300 + x = -314.96031496 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 = -314.96031496 + -300 Combine like terms: 300 + -300 = 0 0 + x = -314.96031496 + -300 x = -314.96031496 + -300 Combine like terms: -314.96031496 + -300 = -614.96031496 x = -614.96031496 Simplifying x = -614.96031496Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.96031496, -614.96031496}
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