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Simplifying x(x + 2) + 5(x) = 46 Reorder the terms: x(2 + x) + 5(x) = 46 (2 * x + x * x) + 5(x) = 46 (2x + x2) + 5(x) = 46 Reorder the terms: 2x + 5x + x2 = 46 Combine like terms: 2x + 5x = 7x 7x + x2 = 46 Solving 7x + x2 = 46 Solving for variable 'x'. Reorder the terms: -46 + 7x + x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -46 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + 7x + 46 + x2 = 0 + 46 Reorder the terms: -46 + 46 + 7x + x2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + 7x + x2 = 0 + 46 7x + x2 = 0 + 46 Combine like terms: 0 + 46 = 46 7x + x2 = 46 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 46 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 46 + 12.25 Combine like terms: 46 + 12.25 = 58.25 12.25 + 7x + x2 = 58.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (x + 3.5) equal to 7.632168761 and -7.632168761.Subproblem 1
x + 3.5 = 7.632168761 Simplifying x + 3.5 = 7.632168761 Reorder the terms: 3.5 + x = 7.632168761 Solving 3.5 + x = 7.632168761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 7.632168761 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 7.632168761 + -3.5 x = 7.632168761 + -3.5 Combine like terms: 7.632168761 + -3.5 = 4.132168761 x = 4.132168761 Simplifying x = 4.132168761Subproblem 2
x + 3.5 = -7.632168761 Simplifying x + 3.5 = -7.632168761 Reorder the terms: 3.5 + x = -7.632168761 Solving 3.5 + x = -7.632168761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -7.632168761 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -7.632168761 + -3.5 x = -7.632168761 + -3.5 Combine like terms: -7.632168761 + -3.5 = -11.132168761 x = -11.132168761 Simplifying x = -11.132168761Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.132168761, -11.132168761}
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