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Simplifying 21 = x2 + -12x + -2 Reorder the terms: 21 = -2 + -12x + x2 Solving 21 = -2 + -12x + x2 Solving for variable 'x'. Combine like terms: 21 + 2 = 23 23 + 12x + -1x2 = -2 + -12x + x2 + 2 + 12x + -1x2 Reorder the terms: 23 + 12x + -1x2 = -2 + 2 + -12x + 12x + x2 + -1x2 Combine like terms: -2 + 2 = 0 23 + 12x + -1x2 = 0 + -12x + 12x + x2 + -1x2 23 + 12x + -1x2 = -12x + 12x + x2 + -1x2 Combine like terms: -12x + 12x = 0 23 + 12x + -1x2 = 0 + x2 + -1x2 23 + 12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 23 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -23 + -12x + x2 = 0 Move the constant term to the right: Add '23' to each side of the equation. -23 + -12x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + -12x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -12x + x2 = 0 + 23 -12x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 -12x + x2 = 23 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 23 + 36 Reorder the terms: 36 + -12x + x2 = 23 + 36 Combine like terms: 23 + 36 = 59 36 + -12x + x2 = 59 Factor a perfect square on the left side: (x + -6)(x + -6) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (x + -6) equal to 7.681145748 and -7.681145748.Subproblem 1
x + -6 = 7.681145748 Simplifying x + -6 = 7.681145748 Reorder the terms: -6 + x = 7.681145748 Solving -6 + x = 7.681145748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 7.681145748 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.681145748 + 6 x = 7.681145748 + 6 Combine like terms: 7.681145748 + 6 = 13.681145748 x = 13.681145748 Simplifying x = 13.681145748Subproblem 2
x + -6 = -7.681145748 Simplifying x + -6 = -7.681145748 Reorder the terms: -6 + x = -7.681145748 Solving -6 + x = -7.681145748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -7.681145748 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.681145748 + 6 x = -7.681145748 + 6 Combine like terms: -7.681145748 + 6 = -1.681145748 x = -1.681145748 Simplifying x = -1.681145748Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.681145748, -1.681145748}
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