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Simplifying x2 + 10x + 21 = 1225 Reorder the terms: 21 + 10x + x2 = 1225 Solving 21 + 10x + x2 = 1225 Solving for variable 'x'. Reorder the terms: 21 + -1225 + 10x + x2 = 1225 + -1225 Combine like terms: 21 + -1225 = -1204 -1204 + 10x + x2 = 1225 + -1225 Combine like terms: 1225 + -1225 = 0 -1204 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1204' to each side of the equation. -1204 + 10x + 1204 + x2 = 0 + 1204 Reorder the terms: -1204 + 1204 + 10x + x2 = 0 + 1204 Combine like terms: -1204 + 1204 = 0 0 + 10x + x2 = 0 + 1204 10x + x2 = 0 + 1204 Combine like terms: 0 + 1204 = 1204 10x + x2 = 1204 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 = 1204 + 25 Reorder the terms: 25 + 10x + x2 = 1204 + 25 Combine like terms: 1204 + 25 = 1229 25 + 10x + x2 = 1229 Factor a perfect square on the left side: (x + 5)(x + 5) = 1229 Calculate the square root of the right side: 35.057096286 Break this problem into two subproblems by setting (x + 5) equal to 35.057096286 and -35.057096286.Subproblem 1
x + 5 = 35.057096286 Simplifying x + 5 = 35.057096286 Reorder the terms: 5 + x = 35.057096286 Solving 5 + x = 35.057096286 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 = 35.057096286 + -5 Combine like terms: 5 + -5 = 0 0 + x = 35.057096286 + -5 x = 35.057096286 + -5 Combine like terms: 35.057096286 + -5 = 30.057096286 x = 30.057096286 Simplifying x = 30.057096286Subproblem 2
x + 5 = -35.057096286 Simplifying x + 5 = -35.057096286 Reorder the terms: 5 + x = -35.057096286 Solving 5 + x = -35.057096286 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 = -35.057096286 + -5 Combine like terms: 5 + -5 = 0 0 + x = -35.057096286 + -5 x = -35.057096286 + -5 Combine like terms: -35.057096286 + -5 = -40.057096286 x = -40.057096286 Simplifying x = -40.057096286Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.057096286, -40.057096286}
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