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Simplifying x2 + 21x + -9972 = 0 Reorder the terms: -9972 + 21x + x2 = 0 Solving -9972 + 21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '9972' to each side of the equation. -9972 + 21x + 9972 + x2 = 0 + 9972 Reorder the terms: -9972 + 9972 + 21x + x2 = 0 + 9972 Combine like terms: -9972 + 9972 = 0 0 + 21x + x2 = 0 + 9972 21x + x2 = 0 + 9972 Combine like terms: 0 + 9972 = 9972 21x + x2 = 9972 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 = 9972 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 9972 + 110.25 Combine like terms: 9972 + 110.25 = 10082.25 110.25 + 21x + x2 = 10082.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 10082.25 Calculate the square root of the right side: 100.410407827 Break this problem into two subproblems by setting (x + 10.5) equal to 100.410407827 and -100.410407827.Subproblem 1
x + 10.5 = 100.410407827 Simplifying x + 10.5 = 100.410407827 Reorder the terms: 10.5 + x = 100.410407827 Solving 10.5 + x = 100.410407827 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 = 100.410407827 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 100.410407827 + -10.5 x = 100.410407827 + -10.5 Combine like terms: 100.410407827 + -10.5 = 89.910407827 x = 89.910407827 Simplifying x = 89.910407827Subproblem 2
x + 10.5 = -100.410407827 Simplifying x + 10.5 = -100.410407827 Reorder the terms: 10.5 + x = -100.410407827 Solving 10.5 + x = -100.410407827 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 = -100.410407827 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -100.410407827 + -10.5 x = -100.410407827 + -10.5 Combine like terms: -100.410407827 + -10.5 = -110.910407827 x = -110.910407827 Simplifying x = -110.910407827Solution
The solution to the problem is based on the solutions from the subproblems. x = {89.910407827, -110.910407827}
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