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Simplifying 2x2 + -5x = 148 Reorder the terms: -5x + 2x2 = 148 Solving -5x + 2x2 = 148 Solving for variable 'x'. Reorder the terms: -148 + -5x + 2x2 = 148 + -148 Combine like terms: 148 + -148 = 0 -148 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -74 + -2.5x + x2 = 0 Move the constant term to the right: Add '74' to each side of the equation. -74 + -2.5x + 74 + x2 = 0 + 74 Reorder the terms: -74 + 74 + -2.5x + x2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + -2.5x + x2 = 0 + 74 -2.5x + x2 = 0 + 74 Combine like terms: 0 + 74 = 74 -2.5x + x2 = 74 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 = 74 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 74 + 1.5625 Combine like terms: 74 + 1.5625 = 75.5625 1.5625 + -2.5x + x2 = 75.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 75.5625 Calculate the square root of the right side: 8.692669325 Break this problem into two subproblems by setting (x + -1.25) equal to 8.692669325 and -8.692669325.Subproblem 1
x + -1.25 = 8.692669325 Simplifying x + -1.25 = 8.692669325 Reorder the terms: -1.25 + x = 8.692669325 Solving -1.25 + x = 8.692669325 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 = 8.692669325 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 8.692669325 + 1.25 x = 8.692669325 + 1.25 Combine like terms: 8.692669325 + 1.25 = 9.942669325 x = 9.942669325 Simplifying x = 9.942669325Subproblem 2
x + -1.25 = -8.692669325 Simplifying x + -1.25 = -8.692669325 Reorder the terms: -1.25 + x = -8.692669325 Solving -1.25 + x = -8.692669325 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 = -8.692669325 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -8.692669325 + 1.25 x = -8.692669325 + 1.25 Combine like terms: -8.692669325 + 1.25 = -7.442669325 x = -7.442669325 Simplifying x = -7.442669325Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.942669325, -7.442669325}
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