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Simplifying x2 + 21x = -16 Reorder the terms: 21x + x2 = -16 Solving 21x + x2 = -16 Solving for variable 'x'. Reorder the terms: 16 + 21x + x2 = -16 + 16 Combine like terms: -16 + 16 = 0 16 + 21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 21x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + 21x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 21x + x2 = 0 + -16 21x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 21x + x2 = -16 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 = -16 + 110.25 Reorder the terms: 110.25 + 21x + x2 = -16 + 110.25 Combine like terms: -16 + 110.25 = 94.25 110.25 + 21x + x2 = 94.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 94.25 Calculate the square root of the right side: 9.708243919 Break this problem into two subproblems by setting (x + 10.5) equal to 9.708243919 and -9.708243919.Subproblem 1
x + 10.5 = 9.708243919 Simplifying x + 10.5 = 9.708243919 Reorder the terms: 10.5 + x = 9.708243919 Solving 10.5 + x = 9.708243919 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 = 9.708243919 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 9.708243919 + -10.5 x = 9.708243919 + -10.5 Combine like terms: 9.708243919 + -10.5 = -0.791756081 x = -0.791756081 Simplifying x = -0.791756081Subproblem 2
x + 10.5 = -9.708243919 Simplifying x + 10.5 = -9.708243919 Reorder the terms: 10.5 + x = -9.708243919 Solving 10.5 + x = -9.708243919 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 = -9.708243919 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -9.708243919 + -10.5 x = -9.708243919 + -10.5 Combine like terms: -9.708243919 + -10.5 = -20.208243919 x = -20.208243919 Simplifying x = -20.208243919Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.791756081, -20.208243919}
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