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Simplifying x2 + -2.5x + -44 = 0 Reorder the terms: -44 + -2.5x + x2 = 0 Solving -44 + -2.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + -2.5x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + -2.5x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -2.5x + x2 = 0 + 44 -2.5x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 -2.5x + x2 = 44 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 = 44 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 44 + 1.5625 Combine like terms: 44 + 1.5625 = 45.5625 1.5625 + -2.5x + x2 = 45.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 45.5625 Calculate the square root of the right side: 6.75 Break this problem into two subproblems by setting (x + -1.25) equal to 6.75 and -6.75.Subproblem 1
x + -1.25 = 6.75 Simplifying x + -1.25 = 6.75 Reorder the terms: -1.25 + x = 6.75 Solving -1.25 + x = 6.75 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 = 6.75 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 6.75 + 1.25 x = 6.75 + 1.25 Combine like terms: 6.75 + 1.25 = 8 x = 8 Simplifying x = 8Subproblem 2
x + -1.25 = -6.75 Simplifying x + -1.25 = -6.75 Reorder the terms: -1.25 + x = -6.75 Solving -1.25 + x = -6.75 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 = -6.75 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -6.75 + 1.25 x = -6.75 + 1.25 Combine like terms: -6.75 + 1.25 = -5.5 x = -5.5 Simplifying x = -5.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, -5.5}
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