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Simplifying x2 + -21x + -78 = 0 Reorder the terms: -78 + -21x + x2 = 0 Solving -78 + -21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '78' to each side of the equation. -78 + -21x + 78 + x2 = 0 + 78 Reorder the terms: -78 + 78 + -21x + x2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + -21x + x2 = 0 + 78 -21x + x2 = 0 + 78 Combine like terms: 0 + 78 = 78 -21x + x2 = 78 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 = 78 + 110.25 Reorder the terms: 110.25 + -21x + x2 = 78 + 110.25 Combine like terms: 78 + 110.25 = 188.25 110.25 + -21x + x2 = 188.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 188.25 Calculate the square root of the right side: 13.720422734 Break this problem into two subproblems by setting (x + -10.5) equal to 13.720422734 and -13.720422734.Subproblem 1
x + -10.5 = 13.720422734 Simplifying x + -10.5 = 13.720422734 Reorder the terms: -10.5 + x = 13.720422734 Solving -10.5 + x = 13.720422734 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 = 13.720422734 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 13.720422734 + 10.5 x = 13.720422734 + 10.5 Combine like terms: 13.720422734 + 10.5 = 24.220422734 x = 24.220422734 Simplifying x = 24.220422734Subproblem 2
x + -10.5 = -13.720422734 Simplifying x + -10.5 = -13.720422734 Reorder the terms: -10.5 + x = -13.720422734 Solving -10.5 + x = -13.720422734 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 = -13.720422734 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -13.720422734 + 10.5 x = -13.720422734 + 10.5 Combine like terms: -13.720422734 + 10.5 = -3.220422734 x = -3.220422734 Simplifying x = -3.220422734Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.220422734, -3.220422734}
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