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Simplifying x2 + 10x + 21 = 122500 Reorder the terms: 21 + 10x + x2 = 122500 Solving 21 + 10x + x2 = 122500 Solving for variable 'x'. Reorder the terms: 21 + -122500 + 10x + x2 = 122500 + -122500 Combine like terms: 21 + -122500 = -122479 -122479 + 10x + x2 = 122500 + -122500 Combine like terms: 122500 + -122500 = 0 -122479 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '122479' to each side of the equation. -122479 + 10x + 122479 + x2 = 0 + 122479 Reorder the terms: -122479 + 122479 + 10x + x2 = 0 + 122479 Combine like terms: -122479 + 122479 = 0 0 + 10x + x2 = 0 + 122479 10x + x2 = 0 + 122479 Combine like terms: 0 + 122479 = 122479 10x + x2 = 122479 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 122479 + 25 Reorder the terms: 25 + 10x + x2 = 122479 + 25 Combine like terms: 122479 + 25 = 122504 25 + 10x + x2 = 122504 Factor a perfect square on the left side: (x + 5)(x + 5) = 122504 Calculate the square root of the right side: 350.005714239 Break this problem into two subproblems by setting (x + 5) equal to 350.005714239 and -350.005714239.Subproblem 1
x + 5 = 350.005714239 Simplifying x + 5 = 350.005714239 Reorder the terms: 5 + x = 350.005714239 Solving 5 + x = 350.005714239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 350.005714239 + -5 Combine like terms: 5 + -5 = 0 0 + x = 350.005714239 + -5 x = 350.005714239 + -5 Combine like terms: 350.005714239 + -5 = 345.005714239 x = 345.005714239 Simplifying x = 345.005714239Subproblem 2
x + 5 = -350.005714239 Simplifying x + 5 = -350.005714239 Reorder the terms: 5 + x = -350.005714239 Solving 5 + x = -350.005714239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -350.005714239 + -5 Combine like terms: 5 + -5 = 0 0 + x = -350.005714239 + -5 x = -350.005714239 + -5 Combine like terms: -350.005714239 + -5 = -355.005714239 x = -355.005714239 Simplifying x = -355.005714239Solution
The solution to the problem is based on the solutions from the subproblems. x = {345.005714239, -355.005714239}
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