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Simplifying 4x(x + -600) = 3765 Reorder the terms: 4x(-600 + x) = 3765 (-600 * 4x + x * 4x) = 3765 (-2400x + 4x2) = 3765 Solving -2400x + 4x2 = 3765 Solving for variable 'x'. Reorder the terms: -3765 + -2400x + 4x2 = 3765 + -3765 Combine like terms: 3765 + -3765 = 0 -3765 + -2400x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -941.25 + -600x + x2 = 0 Move the constant term to the right: Add '941.25' to each side of the equation. -941.25 + -600x + 941.25 + x2 = 0 + 941.25 Reorder the terms: -941.25 + 941.25 + -600x + x2 = 0 + 941.25 Combine like terms: -941.25 + 941.25 = 0.00 0.00 + -600x + x2 = 0 + 941.25 -600x + x2 = 0 + 941.25 Combine like terms: 0 + 941.25 = 941.25 -600x + x2 = 941.25 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 = 941.25 + 90000 Reorder the terms: 90000 + -600x + x2 = 941.25 + 90000 Combine like terms: 941.25 + 90000 = 90941.25 90000 + -600x + x2 = 90941.25 Factor a perfect square on the left side: (x + -300)(x + -300) = 90941.25 Calculate the square root of the right side: 301.564669681 Break this problem into two subproblems by setting (x + -300) equal to 301.564669681 and -301.564669681.Subproblem 1
x + -300 = 301.564669681 Simplifying x + -300 = 301.564669681 Reorder the terms: -300 + x = 301.564669681 Solving -300 + x = 301.564669681 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 = 301.564669681 + 300 Combine like terms: -300 + 300 = 0 0 + x = 301.564669681 + 300 x = 301.564669681 + 300 Combine like terms: 301.564669681 + 300 = 601.564669681 x = 601.564669681 Simplifying x = 601.564669681Subproblem 2
x + -300 = -301.564669681 Simplifying x + -300 = -301.564669681 Reorder the terms: -300 + x = -301.564669681 Solving -300 + x = -301.564669681 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 = -301.564669681 + 300 Combine like terms: -300 + 300 = 0 0 + x = -301.564669681 + 300 x = -301.564669681 + 300 Combine like terms: -301.564669681 + 300 = -1.564669681 x = -1.564669681 Simplifying x = -1.564669681Solution
The solution to the problem is based on the solutions from the subproblems. x = {601.564669681, -1.564669681}
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