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Simplifying -1x2 + 5x = 2.25 Reorder the terms: 5x + -1x2 = 2.25 Solving 5x + -1x2 = 2.25 Solving for variable 'x'. Reorder the terms: -2.25 + 5x + -1x2 = 2.25 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 -2.25 + 5x + -1x2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2.25 + -5x + x2 = 0.00 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -5x + -2.25 + x2 = 0.00 + -2.25 Reorder the terms: 2.25 + -2.25 + -5x + x2 = 0.00 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -5x + x2 = 0.00 + -2.25 -5x + x2 = 0.00 + -2.25 Combine like terms: 0.00 + -2.25 = -2.25 -5x + x2 = -2.25 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -2.25 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -2.25 + 6.25 Combine like terms: -2.25 + 6.25 = 4 6.25 + -5x + x2 = 4 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (x + -2.5) equal to 2 and -2.Subproblem 1
x + -2.5 = 2 Simplifying x + -2.5 = 2 Reorder the terms: -2.5 + x = 2 Solving -2.5 + x = 2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2 + 2.5 x = 2 + 2.5 Combine like terms: 2 + 2.5 = 4.5 x = 4.5 Simplifying x = 4.5Subproblem 2
x + -2.5 = -2 Simplifying x + -2.5 = -2 Reorder the terms: -2.5 + x = -2 Solving -2.5 + x = -2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2 + 2.5 x = -2 + 2.5 Combine like terms: -2 + 2.5 = 0.5 x = 0.5 Simplifying x = 0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.5, 0.5}
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