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Simplifying x2 + 10x + 21 = 324 Reorder the terms: 21 + 10x + x2 = 324 Solving 21 + 10x + x2 = 324 Solving for variable 'x'. Reorder the terms: 21 + -324 + 10x + x2 = 324 + -324 Combine like terms: 21 + -324 = -303 -303 + 10x + x2 = 324 + -324 Combine like terms: 324 + -324 = 0 -303 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '303' to each side of the equation. -303 + 10x + 303 + x2 = 0 + 303 Reorder the terms: -303 + 303 + 10x + x2 = 0 + 303 Combine like terms: -303 + 303 = 0 0 + 10x + x2 = 0 + 303 10x + x2 = 0 + 303 Combine like terms: 0 + 303 = 303 10x + x2 = 303 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 = 303 + 25 Reorder the terms: 25 + 10x + x2 = 303 + 25 Combine like terms: 303 + 25 = 328 25 + 10x + x2 = 328 Factor a perfect square on the left side: (x + 5)(x + 5) = 328 Calculate the square root of the right side: 18.110770276 Break this problem into two subproblems by setting (x + 5) equal to 18.110770276 and -18.110770276.Subproblem 1
x + 5 = 18.110770276 Simplifying x + 5 = 18.110770276 Reorder the terms: 5 + x = 18.110770276 Solving 5 + x = 18.110770276 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 = 18.110770276 + -5 Combine like terms: 5 + -5 = 0 0 + x = 18.110770276 + -5 x = 18.110770276 + -5 Combine like terms: 18.110770276 + -5 = 13.110770276 x = 13.110770276 Simplifying x = 13.110770276Subproblem 2
x + 5 = -18.110770276 Simplifying x + 5 = -18.110770276 Reorder the terms: 5 + x = -18.110770276 Solving 5 + x = -18.110770276 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 = -18.110770276 + -5 Combine like terms: 5 + -5 = 0 0 + x = -18.110770276 + -5 x = -18.110770276 + -5 Combine like terms: -18.110770276 + -5 = -23.110770276 x = -23.110770276 Simplifying x = -23.110770276Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.110770276, -23.110770276}
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