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Simplifying x2 + 21x = -30 Reorder the terms: 21x + x2 = -30 Solving 21x + x2 = -30 Solving for variable 'x'. Reorder the terms: 30 + 21x + x2 = -30 + 30 Combine like terms: -30 + 30 = 0 30 + 21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + 21x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + 21x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 21x + x2 = 0 + -30 21x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 21x + x2 = -30 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 = -30 + 110.25 Reorder the terms: 110.25 + 21x + x2 = -30 + 110.25 Combine like terms: -30 + 110.25 = 80.25 110.25 + 21x + x2 = 80.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 80.25 Calculate the square root of the right side: 8.958236434 Break this problem into two subproblems by setting (x + 10.5) equal to 8.958236434 and -8.958236434.Subproblem 1
x + 10.5 = 8.958236434 Simplifying x + 10.5 = 8.958236434 Reorder the terms: 10.5 + x = 8.958236434 Solving 10.5 + x = 8.958236434 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 = 8.958236434 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 8.958236434 + -10.5 x = 8.958236434 + -10.5 Combine like terms: 8.958236434 + -10.5 = -1.541763566 x = -1.541763566 Simplifying x = -1.541763566Subproblem 2
x + 10.5 = -8.958236434 Simplifying x + 10.5 = -8.958236434 Reorder the terms: 10.5 + x = -8.958236434 Solving 10.5 + x = -8.958236434 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 = -8.958236434 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -8.958236434 + -10.5 x = -8.958236434 + -10.5 Combine like terms: -8.958236434 + -10.5 = -19.458236434 x = -19.458236434 Simplifying x = -19.458236434Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.541763566, -19.458236434}
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