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Simplifying (5x + 2x * x) = 500 Multiply x * x (5x + 2x2) = 500 Remove parenthesis around (5x + 2x2) 5x + 2x2 = 500 Solving 5x + 2x2 = 500 Solving for variable 'x'. Reorder the terms: -500 + 5x + 2x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -500 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -250 + 2.5x + x2 = 0 Move the constant term to the right: Add '250' to each side of the equation. -250 + 2.5x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + 2.5x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + 2.5x + x2 = 0 + 250 2.5x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 2.5x + x2 = 250 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 250 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 250 + 1.5625 Combine like terms: 250 + 1.5625 = 251.5625 1.5625 + 2.5x + x2 = 251.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 251.5625 Calculate the square root of the right side: 15.860721926 Break this problem into two subproblems by setting (x + 1.25) equal to 15.860721926 and -15.860721926.Subproblem 1
x + 1.25 = 15.860721926 Simplifying x + 1.25 = 15.860721926 Reorder the terms: 1.25 + x = 15.860721926 Solving 1.25 + x = 15.860721926 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 15.860721926 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 15.860721926 + -1.25 x = 15.860721926 + -1.25 Combine like terms: 15.860721926 + -1.25 = 14.610721926 x = 14.610721926 Simplifying x = 14.610721926Subproblem 2
x + 1.25 = -15.860721926 Simplifying x + 1.25 = -15.860721926 Reorder the terms: 1.25 + x = -15.860721926 Solving 1.25 + x = -15.860721926 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -15.860721926 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -15.860721926 + -1.25 x = -15.860721926 + -1.25 Combine like terms: -15.860721926 + -1.25 = -17.110721926 x = -17.110721926 Simplifying x = -17.110721926Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.610721926, -17.110721926}
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