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Simplifying x2 + 10x + 21 = 400 Reorder the terms: 21 + 10x + x2 = 400 Solving 21 + 10x + x2 = 400 Solving for variable 'x'. Reorder the terms: 21 + -400 + 10x + x2 = 400 + -400 Combine like terms: 21 + -400 = -379 -379 + 10x + x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -379 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '379' to each side of the equation. -379 + 10x + 379 + x2 = 0 + 379 Reorder the terms: -379 + 379 + 10x + x2 = 0 + 379 Combine like terms: -379 + 379 = 0 0 + 10x + x2 = 0 + 379 10x + x2 = 0 + 379 Combine like terms: 0 + 379 = 379 10x + x2 = 379 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 = 379 + 25 Reorder the terms: 25 + 10x + x2 = 379 + 25 Combine like terms: 379 + 25 = 404 25 + 10x + x2 = 404 Factor a perfect square on the left side: (x + 5)(x + 5) = 404 Calculate the square root of the right side: 20.099751242 Break this problem into two subproblems by setting (x + 5) equal to 20.099751242 and -20.099751242.Subproblem 1
x + 5 = 20.099751242 Simplifying x + 5 = 20.099751242 Reorder the terms: 5 + x = 20.099751242 Solving 5 + x = 20.099751242 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 = 20.099751242 + -5 Combine like terms: 5 + -5 = 0 0 + x = 20.099751242 + -5 x = 20.099751242 + -5 Combine like terms: 20.099751242 + -5 = 15.099751242 x = 15.099751242 Simplifying x = 15.099751242Subproblem 2
x + 5 = -20.099751242 Simplifying x + 5 = -20.099751242 Reorder the terms: 5 + x = -20.099751242 Solving 5 + x = -20.099751242 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 = -20.099751242 + -5 Combine like terms: 5 + -5 = 0 0 + x = -20.099751242 + -5 x = -20.099751242 + -5 Combine like terms: -20.099751242 + -5 = -25.099751242 x = -25.099751242 Simplifying x = -25.099751242Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.099751242, -25.099751242}
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