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Simplifying 44 = x(x + 2.5) Reorder the terms: 44 = x(2.5 + x) 44 = (2.5 * x + x * x) 44 = (2.5x + x2) Solving 44 = 2.5x + x2 Solving for variable 'x'. Reorder the terms: 44 + -2.5x + -1x2 = 2.5x + -2.5x + x2 + -1x2 Combine like terms: 2.5x + -2.5x = 0.0 44 + -2.5x + -1x2 = 0.0 + x2 + -1x2 44 + -2.5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 44 + -2.5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -44 + 2.5x + x2 = 0 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 = 5.5 x = 5.5 Simplifying x = 5.5Subproblem 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 = -8 x = -8 Simplifying x = -8Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.5, -8}
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