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Simplifying 2x2 + 5x = 252 Reorder the terms: 5x + 2x2 = 252 Solving 5x + 2x2 = 252 Solving for variable 'x'. Reorder the terms: -252 + 5x + 2x2 = 252 + -252 Combine like terms: 252 + -252 = 0 -252 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -126 + 2.5x + x2 = 0 Move the constant term to the right: Add '126' to each side of the equation. -126 + 2.5x + 126 + x2 = 0 + 126 Reorder the terms: -126 + 126 + 2.5x + x2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + 2.5x + x2 = 0 + 126 2.5x + x2 = 0 + 126 Combine like terms: 0 + 126 = 126 2.5x + x2 = 126 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 = 126 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 126 + 1.5625 Combine like terms: 126 + 1.5625 = 127.5625 1.5625 + 2.5x + x2 = 127.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 127.5625 Calculate the square root of the right side: 11.294356998 Break this problem into two subproblems by setting (x + 1.25) equal to 11.294356998 and -11.294356998.Subproblem 1
x + 1.25 = 11.294356998 Simplifying x + 1.25 = 11.294356998 Reorder the terms: 1.25 + x = 11.294356998 Solving 1.25 + x = 11.294356998 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 = 11.294356998 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 11.294356998 + -1.25 x = 11.294356998 + -1.25 Combine like terms: 11.294356998 + -1.25 = 10.044356998 x = 10.044356998 Simplifying x = 10.044356998Subproblem 2
x + 1.25 = -11.294356998 Simplifying x + 1.25 = -11.294356998 Reorder the terms: 1.25 + x = -11.294356998 Solving 1.25 + x = -11.294356998 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 = -11.294356998 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -11.294356998 + -1.25 x = -11.294356998 + -1.25 Combine like terms: -11.294356998 + -1.25 = -12.544356998 x = -12.544356998 Simplifying x = -12.544356998Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.044356998, -12.544356998}
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