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Simplifying x2 + 10x + 21 = 225 Reorder the terms: 21 + 10x + x2 = 225 Solving 21 + 10x + x2 = 225 Solving for variable 'x'. Reorder the terms: 21 + -225 + 10x + x2 = 225 + -225 Combine like terms: 21 + -225 = -204 -204 + 10x + x2 = 225 + -225 Combine like terms: 225 + -225 = 0 -204 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '204' to each side of the equation. -204 + 10x + 204 + x2 = 0 + 204 Reorder the terms: -204 + 204 + 10x + x2 = 0 + 204 Combine like terms: -204 + 204 = 0 0 + 10x + x2 = 0 + 204 10x + x2 = 0 + 204 Combine like terms: 0 + 204 = 204 10x + x2 = 204 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 = 204 + 25 Reorder the terms: 25 + 10x + x2 = 204 + 25 Combine like terms: 204 + 25 = 229 25 + 10x + x2 = 229 Factor a perfect square on the left side: (x + 5)(x + 5) = 229 Calculate the square root of the right side: 15.13274595 Break this problem into two subproblems by setting (x + 5) equal to 15.13274595 and -15.13274595.Subproblem 1
x + 5 = 15.13274595 Simplifying x + 5 = 15.13274595 Reorder the terms: 5 + x = 15.13274595 Solving 5 + x = 15.13274595 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 = 15.13274595 + -5 Combine like terms: 5 + -5 = 0 0 + x = 15.13274595 + -5 x = 15.13274595 + -5 Combine like terms: 15.13274595 + -5 = 10.13274595 x = 10.13274595 Simplifying x = 10.13274595Subproblem 2
x + 5 = -15.13274595 Simplifying x + 5 = -15.13274595 Reorder the terms: 5 + x = -15.13274595 Solving 5 + x = -15.13274595 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 = -15.13274595 + -5 Combine like terms: 5 + -5 = 0 0 + x = -15.13274595 + -5 x = -15.13274595 + -5 Combine like terms: -15.13274595 + -5 = -20.13274595 x = -20.13274595 Simplifying x = -20.13274595Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.13274595, -20.13274595}
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