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Simplifying x2 + -21x + -108 = 0 Reorder the terms: -108 + -21x + x2 = 0 Solving -108 + -21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '108' to each side of the equation. -108 + -21x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + -21x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + -21x + x2 = 0 + 108 -21x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 -21x + x2 = 108 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 = 108 + 110.25 Reorder the terms: 110.25 + -21x + x2 = 108 + 110.25 Combine like terms: 108 + 110.25 = 218.25 110.25 + -21x + x2 = 218.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 218.25 Calculate the square root of the right side: 14.773286703 Break this problem into two subproblems by setting (x + -10.5) equal to 14.773286703 and -14.773286703.Subproblem 1
x + -10.5 = 14.773286703 Simplifying x + -10.5 = 14.773286703 Reorder the terms: -10.5 + x = 14.773286703 Solving -10.5 + x = 14.773286703 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 = 14.773286703 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 14.773286703 + 10.5 x = 14.773286703 + 10.5 Combine like terms: 14.773286703 + 10.5 = 25.273286703 x = 25.273286703 Simplifying x = 25.273286703Subproblem 2
x + -10.5 = -14.773286703 Simplifying x + -10.5 = -14.773286703 Reorder the terms: -10.5 + x = -14.773286703 Solving -10.5 + x = -14.773286703 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 = -14.773286703 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -14.773286703 + 10.5 x = -14.773286703 + 10.5 Combine like terms: -14.773286703 + 10.5 = -4.273286703 x = -4.273286703 Simplifying x = -4.273286703Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.273286703, -4.273286703}
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