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Simplifying x2 + 21x + 110.25 = 0 Reorder the terms: 110.25 + 21x + x2 = 0 Solving 110.25 + 21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-110.25' to each side of the equation. 110.25 + 21x + -110.25 + x2 = 0 + -110.25 Reorder the terms: 110.25 + -110.25 + 21x + x2 = 0 + -110.25 Combine like terms: 110.25 + -110.25 = 0.00 0.00 + 21x + x2 = 0 + -110.25 21x + x2 = 0 + -110.25 Combine like terms: 0 + -110.25 = -110.25 21x + x2 = -110.25 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 = -110.25 + 110.25 Reorder the terms: 110.25 + 21x + x2 = -110.25 + 110.25 Combine like terms: -110.25 + 110.25 = 0.00 110.25 + 21x + x2 = 0.00 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + 10.5) equal to 0.00 and 0.00.Subproblem 1
x + 10.5 = 0.00 Simplifying x + 10.5 = 0.00 Reorder the terms: 10.5 + x = 0.00 Solving 10.5 + x = 0.00 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 = 0.00 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 0.00 + -10.5 x = 0.00 + -10.5 Combine like terms: 0.00 + -10.5 = -10.5 x = -10.5 Simplifying x = -10.5Subproblem 2
x + 10.5 = 0.00 Simplifying x + 10.5 = 0.00 Reorder the terms: 10.5 + x = 0.00 Solving 10.5 + x = 0.00 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 = 0.00 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 0.00 + -10.5 x = 0.00 + -10.5 Combine like terms: 0.00 + -10.5 = -10.5 x = -10.5 Simplifying x = -10.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-10.5, -10.5}
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