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Simplifying x2 + 21x + 108 = 2 Reorder the terms: 108 + 21x + x2 = 2 Solving 108 + 21x + x2 = 2 Solving for variable 'x'. Reorder the terms: 108 + -2 + 21x + x2 = 2 + -2 Combine like terms: 108 + -2 = 106 106 + 21x + x2 = 2 + -2 Combine like terms: 2 + -2 = 0 106 + 21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-106' to each side of the equation. 106 + 21x + -106 + x2 = 0 + -106 Reorder the terms: 106 + -106 + 21x + x2 = 0 + -106 Combine like terms: 106 + -106 = 0 0 + 21x + x2 = 0 + -106 21x + x2 = 0 + -106 Combine like terms: 0 + -106 = -106 21x + x2 = -106 The x term is 21x. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21x + 110.25 + x2 = -106 + 110.25 Reorder the terms: 110.25 + 21x + x2 = -106 + 110.25 Combine like terms: -106 + 110.25 = 4.25 110.25 + 21x + x2 = 4.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + 10.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + 10.5 = 2.061552813 Simplifying x + 10.5 = 2.061552813 Reorder the terms: 10.5 + x = 2.061552813 Solving 10.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 2.061552813 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 2.061552813 + -10.5 x = 2.061552813 + -10.5 Combine like terms: 2.061552813 + -10.5 = -8.438447187 x = -8.438447187 Simplifying x = -8.438447187Subproblem 2
x + 10.5 = -2.061552813 Simplifying x + 10.5 = -2.061552813 Reorder the terms: 10.5 + x = -2.061552813 Solving 10.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -2.061552813 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -2.061552813 + -10.5 x = -2.061552813 + -10.5 Combine like terms: -2.061552813 + -10.5 = -12.561552813 x = -12.561552813 Simplifying x = -12.561552813Solution
The solution to the problem is based on the solutions from the subproblems. x = {-8.438447187, -12.561552813}
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