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Simplifying 21 = x2 + -2x Reorder the terms: 21 = -2x + x2 Solving 21 = -2x + x2 Solving for variable 'x'. Reorder the terms: 21 + 2x + -1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 21 + 2x + -1x2 = 0 + x2 + -1x2 21 + 2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 21 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -21 + -2x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -2x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -2x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -2x + x2 = 0 + 21 -2x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -2x + x2 = 21 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 21 + 1 Reorder the terms: 1 + -2x + x2 = 21 + 1 Combine like terms: 21 + 1 = 22 1 + -2x + x2 = 22 Factor a perfect square on the left side: (x + -1)(x + -1) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (x + -1) equal to 4.69041576 and -4.69041576.Subproblem 1
x + -1 = 4.69041576 Simplifying x + -1 = 4.69041576 Reorder the terms: -1 + x = 4.69041576 Solving -1 + x = 4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 4.69041576 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.69041576 + 1 x = 4.69041576 + 1 Combine like terms: 4.69041576 + 1 = 5.69041576 x = 5.69041576 Simplifying x = 5.69041576Subproblem 2
x + -1 = -4.69041576 Simplifying x + -1 = -4.69041576 Reorder the terms: -1 + x = -4.69041576 Solving -1 + x = -4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -4.69041576 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.69041576 + 1 x = -4.69041576 + 1 Combine like terms: -4.69041576 + 1 = -3.69041576 x = -3.69041576 Simplifying x = -3.69041576Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.69041576, -3.69041576}
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