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Simplifying x(5)(x + 1) = 22 Reorder the terms: x * 5(1 + x) = 22 Reorder the terms for easier multiplication: 5x(1 + x) = 22 (1 * 5x + x * 5x) = 22 (5x + 5x2) = 22 Solving 5x + 5x2 = 22 Solving for variable 'x'. Reorder the terms: -22 + 5x + 5x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -22 + 5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.4 + x + x2 = 0 Move the constant term to the right: Add '4.4' to each side of the equation. -4.4 + x + 4.4 + x2 = 0 + 4.4 Reorder the terms: -4.4 + 4.4 + x + x2 = 0 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + x + x2 = 0 + 4.4 x + x2 = 0 + 4.4 Combine like terms: 0 + 4.4 = 4.4 x + x2 = 4.4 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 4.4 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 4.4 + 0.25 Combine like terms: 4.4 + 0.25 = 4.65 1.25 + x2 = 4.65 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 4.65 Calculate the square root of the right side: 2.156385865 Break this problem into two subproblems by setting (x + 0.5) equal to 2.156385865 and -2.156385865.Subproblem 1
x + 0.5 = 2.156385865 Simplifying x + 0.5 = 2.156385865 Reorder the terms: 0.5 + x = 2.156385865 Solving 0.5 + x = 2.156385865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.156385865 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.156385865 + -0.5 x = 2.156385865 + -0.5 Combine like terms: 2.156385865 + -0.5 = 1.656385865 x = 1.656385865 Simplifying x = 1.656385865Subproblem 2
x + 0.5 = -2.156385865 Simplifying x + 0.5 = -2.156385865 Reorder the terms: 0.5 + x = -2.156385865 Solving 0.5 + x = -2.156385865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.156385865 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.156385865 + -0.5 x = -2.156385865 + -0.5 Combine like terms: -2.156385865 + -0.5 = -2.656385865 x = -2.656385865 Simplifying x = -2.656385865Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.656385865, -2.656385865}
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