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Simplifying 2x2 + -5x = 146 Reorder the terms: -5x + 2x2 = 146 Solving -5x + 2x2 = 146 Solving for variable 'x'. Reorder the terms: -146 + -5x + 2x2 = 146 + -146 Combine like terms: 146 + -146 = 0 -146 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -73 + -2.5x + x2 = 0 Move the constant term to the right: Add '73' to each side of the equation. -73 + -2.5x + 73 + x2 = 0 + 73 Reorder the terms: -73 + 73 + -2.5x + x2 = 0 + 73 Combine like terms: -73 + 73 = 0 0 + -2.5x + x2 = 0 + 73 -2.5x + x2 = 0 + 73 Combine like terms: 0 + 73 = 73 -2.5x + x2 = 73 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 = 73 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 73 + 1.5625 Combine like terms: 73 + 1.5625 = 74.5625 1.5625 + -2.5x + x2 = 74.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 74.5625 Calculate the square root of the right side: 8.63495802 Break this problem into two subproblems by setting (x + -1.25) equal to 8.63495802 and -8.63495802.Subproblem 1
x + -1.25 = 8.63495802 Simplifying x + -1.25 = 8.63495802 Reorder the terms: -1.25 + x = 8.63495802 Solving -1.25 + x = 8.63495802 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 = 8.63495802 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 8.63495802 + 1.25 x = 8.63495802 + 1.25 Combine like terms: 8.63495802 + 1.25 = 9.88495802 x = 9.88495802 Simplifying x = 9.88495802Subproblem 2
x + -1.25 = -8.63495802 Simplifying x + -1.25 = -8.63495802 Reorder the terms: -1.25 + x = -8.63495802 Solving -1.25 + x = -8.63495802 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 = -8.63495802 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -8.63495802 + 1.25 x = -8.63495802 + 1.25 Combine like terms: -8.63495802 + 1.25 = -7.38495802 x = -7.38495802 Simplifying x = -7.38495802Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.88495802, -7.38495802}
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