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Simplifying x2 + 21x + -77 = 0 Reorder the terms: -77 + 21x + x2 = 0 Solving -77 + 21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + 21x + 77 + x2 = 0 + 77 Reorder the terms: -77 + 77 + 21x + x2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + 21x + x2 = 0 + 77 21x + x2 = 0 + 77 Combine like terms: 0 + 77 = 77 21x + x2 = 77 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 = 77 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 77 + 110.25 Combine like terms: 77 + 110.25 = 187.25 110.25 + 21x + x2 = 187.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 187.25 Calculate the square root of the right side: 13.683932183 Break this problem into two subproblems by setting (x + 10.5) equal to 13.683932183 and -13.683932183.Subproblem 1
x + 10.5 = 13.683932183 Simplifying x + 10.5 = 13.683932183 Reorder the terms: 10.5 + x = 13.683932183 Solving 10.5 + x = 13.683932183 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 = 13.683932183 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 13.683932183 + -10.5 x = 13.683932183 + -10.5 Combine like terms: 13.683932183 + -10.5 = 3.183932183 x = 3.183932183 Simplifying x = 3.183932183Subproblem 2
x + 10.5 = -13.683932183 Simplifying x + 10.5 = -13.683932183 Reorder the terms: 10.5 + x = -13.683932183 Solving 10.5 + x = -13.683932183 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 = -13.683932183 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -13.683932183 + -10.5 x = -13.683932183 + -10.5 Combine like terms: -13.683932183 + -10.5 = -24.183932183 x = -24.183932183 Simplifying x = -24.183932183Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.183932183, -24.183932183}
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