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Simplifying (x + 2) * 2x + 5 = 11(x + 2) Reorder the terms: (2 + x) * 2x + 5 = 11(x + 2) Reorder the terms for easier multiplication: 2x(2 + x) + 5 = 11(x + 2) (2 * 2x + x * 2x) + 5 = 11(x + 2) (4x + 2x2) + 5 = 11(x + 2) Reorder the terms: 5 + 4x + 2x2 = 11(x + 2) Reorder the terms: 5 + 4x + 2x2 = 11(2 + x) 5 + 4x + 2x2 = (2 * 11 + x * 11) 5 + 4x + 2x2 = (22 + 11x) Solving 5 + 4x + 2x2 = 22 + 11x Solving for variable 'x'. Reorder the terms: 5 + -22 + 4x + -11x + 2x2 = 22 + 11x + -22 + -11x Combine like terms: 5 + -22 = -17 -17 + 4x + -11x + 2x2 = 22 + 11x + -22 + -11x Combine like terms: 4x + -11x = -7x -17 + -7x + 2x2 = 22 + 11x + -22 + -11x Reorder the terms: -17 + -7x + 2x2 = 22 + -22 + 11x + -11x Combine like terms: 22 + -22 = 0 -17 + -7x + 2x2 = 0 + 11x + -11x -17 + -7x + 2x2 = 11x + -11x Combine like terms: 11x + -11x = 0 -17 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + -3.5x + 8.5 + x2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + -3.5x + x2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + -3.5x + x2 = 0 + 8.5 -3.5x + x2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 -3.5x + x2 = 8.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 8.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 8.5 + 3.0625 Combine like terms: 8.5 + 3.0625 = 11.5625 3.0625 + -3.5x + x2 = 11.5625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 11.5625 Calculate the square root of the right side: 3.400367627 Break this problem into two subproblems by setting (x + -1.75) equal to 3.400367627 and -3.400367627.Subproblem 1
x + -1.75 = 3.400367627 Simplifying x + -1.75 = 3.400367627 Reorder the terms: -1.75 + x = 3.400367627 Solving -1.75 + x = 3.400367627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 3.400367627 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 3.400367627 + 1.75 x = 3.400367627 + 1.75 Combine like terms: 3.400367627 + 1.75 = 5.150367627 x = 5.150367627 Simplifying x = 5.150367627Subproblem 2
x + -1.75 = -3.400367627 Simplifying x + -1.75 = -3.400367627 Reorder the terms: -1.75 + x = -3.400367627 Solving -1.75 + x = -3.400367627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -3.400367627 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -3.400367627 + 1.75 x = -3.400367627 + 1.75 Combine like terms: -3.400367627 + 1.75 = -1.650367627 x = -1.650367627 Simplifying x = -1.650367627Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.150367627, -1.650367627}
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