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Simplifying 21 = x[x + 2] Reorder the terms: 21 = x[2 + x] 21 = [2 * x + x * x] 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 = 3.69041576 x = 3.69041576 Simplifying x = 3.69041576Subproblem 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 = -5.69041576 x = -5.69041576 Simplifying x = -5.69041576Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.69041576, -5.69041576}
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