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Simplifying x2 + 10x + 21 = 625 Reorder the terms: 21 + 10x + x2 = 625 Solving 21 + 10x + x2 = 625 Solving for variable 'x'. Reorder the terms: 21 + -625 + 10x + x2 = 625 + -625 Combine like terms: 21 + -625 = -604 -604 + 10x + x2 = 625 + -625 Combine like terms: 625 + -625 = 0 -604 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '604' to each side of the equation. -604 + 10x + 604 + x2 = 0 + 604 Reorder the terms: -604 + 604 + 10x + x2 = 0 + 604 Combine like terms: -604 + 604 = 0 0 + 10x + x2 = 0 + 604 10x + x2 = 0 + 604 Combine like terms: 0 + 604 = 604 10x + x2 = 604 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 = 604 + 25 Reorder the terms: 25 + 10x + x2 = 604 + 25 Combine like terms: 604 + 25 = 629 25 + 10x + x2 = 629 Factor a perfect square on the left side: (x + 5)(x + 5) = 629 Calculate the square root of the right side: 25.079872408 Break this problem into two subproblems by setting (x + 5) equal to 25.079872408 and -25.079872408.Subproblem 1
x + 5 = 25.079872408 Simplifying x + 5 = 25.079872408 Reorder the terms: 5 + x = 25.079872408 Solving 5 + x = 25.079872408 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 = 25.079872408 + -5 Combine like terms: 5 + -5 = 0 0 + x = 25.079872408 + -5 x = 25.079872408 + -5 Combine like terms: 25.079872408 + -5 = 20.079872408 x = 20.079872408 Simplifying x = 20.079872408Subproblem 2
x + 5 = -25.079872408 Simplifying x + 5 = -25.079872408 Reorder the terms: 5 + x = -25.079872408 Solving 5 + x = -25.079872408 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 = -25.079872408 + -5 Combine like terms: 5 + -5 = 0 0 + x = -25.079872408 + -5 x = -25.079872408 + -5 Combine like terms: -25.079872408 + -5 = -30.079872408 x = -30.079872408 Simplifying x = -30.079872408Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.079872408, -30.079872408}
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