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Simplifying 2x2 + -4.5x = 10 Reorder the terms: -4.5x + 2x2 = 10 Solving -4.5x + 2x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + -4.5x + 2x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -4.5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5 + -2.25x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -2.25x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -2.25x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2.25x + x2 = 0 + 5 -2.25x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2.25x + x2 = 5 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = 5 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 5 + 1.265625 Combine like terms: 5 + 1.265625 = 6.265625 1.265625 + -2.25x + x2 = 6.265625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 6.265625 Calculate the square root of the right side: 2.503123049 Break this problem into two subproblems by setting (x + -1.125) equal to 2.503123049 and -2.503123049.Subproblem 1
x + -1.125 = 2.503123049 Simplifying x + -1.125 = 2.503123049 Reorder the terms: -1.125 + x = 2.503123049 Solving -1.125 + x = 2.503123049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 2.503123049 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 2.503123049 + 1.125 x = 2.503123049 + 1.125 Combine like terms: 2.503123049 + 1.125 = 3.628123049 x = 3.628123049 Simplifying x = 3.628123049Subproblem 2
x + -1.125 = -2.503123049 Simplifying x + -1.125 = -2.503123049 Reorder the terms: -1.125 + x = -2.503123049 Solving -1.125 + x = -2.503123049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -2.503123049 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -2.503123049 + 1.125 x = -2.503123049 + 1.125 Combine like terms: -2.503123049 + 1.125 = -1.378123049 x = -1.378123049 Simplifying x = -1.378123049Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.628123049, -1.378123049}
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