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Simplifying (5.5 + 2x) * x = 5.1 Reorder the terms for easier multiplication: x(5.5 + 2x) = 5.1 (5.5 * x + 2x * x) = 5.1 (5.5x + 2x2) = 5.1 Solving 5.5x + 2x2 = 5.1 Solving for variable 'x'. Reorder the terms: -5.1 + 5.5x + 2x2 = 5.1 + -5.1 Combine like terms: 5.1 + -5.1 = 0.0 -5.1 + 5.5x + 2x2 = 0.0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.55 + 2.75x + x2 = 0.0 Move the constant term to the right: Add '2.55' to each side of the equation. -2.55 + 2.75x + 2.55 + x2 = 0.0 + 2.55 Reorder the terms: -2.55 + 2.55 + 2.75x + x2 = 0.0 + 2.55 Combine like terms: -2.55 + 2.55 = 0.00 0.00 + 2.75x + x2 = 0.0 + 2.55 2.75x + x2 = 0.0 + 2.55 Combine like terms: 0.0 + 2.55 = 2.55 2.75x + x2 = 2.55 The x term is 2.75x. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75x + 1.890625 + x2 = 2.55 + 1.890625 Reorder the terms: 1.890625 + 2.75x + x2 = 2.55 + 1.890625 Combine like terms: 2.55 + 1.890625 = 4.440625 1.890625 + 2.75x + x2 = 4.440625 Factor a perfect square on the left side: (x + 1.375)(x + 1.375) = 4.440625 Calculate the square root of the right side: 2.107279051 Break this problem into two subproblems by setting (x + 1.375) equal to 2.107279051 and -2.107279051.Subproblem 1
x + 1.375 = 2.107279051 Simplifying x + 1.375 = 2.107279051 Reorder the terms: 1.375 + x = 2.107279051 Solving 1.375 + x = 2.107279051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = 2.107279051 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 2.107279051 + -1.375 x = 2.107279051 + -1.375 Combine like terms: 2.107279051 + -1.375 = 0.732279051 x = 0.732279051 Simplifying x = 0.732279051Subproblem 2
x + 1.375 = -2.107279051 Simplifying x + 1.375 = -2.107279051 Reorder the terms: 1.375 + x = -2.107279051 Solving 1.375 + x = -2.107279051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = -2.107279051 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -2.107279051 + -1.375 x = -2.107279051 + -1.375 Combine like terms: -2.107279051 + -1.375 = -3.482279051 x = -3.482279051 Simplifying x = -3.482279051Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.732279051, -3.482279051}
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