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Simplifying -1x2 + -21x + 68 = 0 Reorder the terms: 68 + -21x + -1x2 = 0 Solving 68 + -21x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -68 + 21x + x2 = 0 Move the constant term to the right: Add '68' to each side of the equation. -68 + 21x + 68 + x2 = 0 + 68 Reorder the terms: -68 + 68 + 21x + x2 = 0 + 68 Combine like terms: -68 + 68 = 0 0 + 21x + x2 = 0 + 68 21x + x2 = 0 + 68 Combine like terms: 0 + 68 = 68 21x + x2 = 68 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 = 68 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 68 + 110.25 Combine like terms: 68 + 110.25 = 178.25 110.25 + 21x + x2 = 178.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 178.25 Calculate the square root of the right side: 13.351029923 Break this problem into two subproblems by setting (x + 10.5) equal to 13.351029923 and -13.351029923.Subproblem 1
x + 10.5 = 13.351029923 Simplifying x + 10.5 = 13.351029923 Reorder the terms: 10.5 + x = 13.351029923 Solving 10.5 + x = 13.351029923 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 = 13.351029923 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 13.351029923 + -10.5 x = 13.351029923 + -10.5 Combine like terms: 13.351029923 + -10.5 = 2.851029923 x = 2.851029923 Simplifying x = 2.851029923Subproblem 2
x + 10.5 = -13.351029923 Simplifying x + 10.5 = -13.351029923 Reorder the terms: 10.5 + x = -13.351029923 Solving 10.5 + x = -13.351029923 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 = -13.351029923 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -13.351029923 + -10.5 x = -13.351029923 + -10.5 Combine like terms: -13.351029923 + -10.5 = -23.851029923 x = -23.851029923 Simplifying x = -23.851029923Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.851029923, -23.851029923}
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