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Simplifying 5 + x(x + 2) = 495 Reorder the terms: 5 + x(2 + x) = 495 5 + (2 * x + x * x) = 495 5 + (2x + x2) = 495 Solving 5 + 2x + x2 = 495 Solving for variable 'x'. Reorder the terms: 5 + -495 + 2x + x2 = 495 + -495 Combine like terms: 5 + -495 = -490 -490 + 2x + x2 = 495 + -495 Combine like terms: 495 + -495 = 0 -490 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '490' to each side of the equation. -490 + 2x + 490 + x2 = 0 + 490 Reorder the terms: -490 + 490 + 2x + x2 = 0 + 490 Combine like terms: -490 + 490 = 0 0 + 2x + x2 = 0 + 490 2x + x2 = 0 + 490 Combine like terms: 0 + 490 = 490 2x + x2 = 490 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 490 + 1 Reorder the terms: 1 + 2x + x2 = 490 + 1 Combine like terms: 490 + 1 = 491 1 + 2x + x2 = 491 Factor a perfect square on the left side: (x + 1)(x + 1) = 491 Calculate the square root of the right side: 22.158519806 Break this problem into two subproblems by setting (x + 1) equal to 22.158519806 and -22.158519806.Subproblem 1
x + 1 = 22.158519806 Simplifying x + 1 = 22.158519806 Reorder the terms: 1 + x = 22.158519806 Solving 1 + x = 22.158519806 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 22.158519806 + -1 Combine like terms: 1 + -1 = 0 0 + x = 22.158519806 + -1 x = 22.158519806 + -1 Combine like terms: 22.158519806 + -1 = 21.158519806 x = 21.158519806 Simplifying x = 21.158519806Subproblem 2
x + 1 = -22.158519806 Simplifying x + 1 = -22.158519806 Reorder the terms: 1 + x = -22.158519806 Solving 1 + x = -22.158519806 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -22.158519806 + -1 Combine like terms: 1 + -1 = 0 0 + x = -22.158519806 + -1 x = -22.158519806 + -1 Combine like terms: -22.158519806 + -1 = -23.158519806 x = -23.158519806 Simplifying x = -23.158519806Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.158519806, -23.158519806}
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