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Simplifying x2 + -1(x + 1) = 21 Reorder the terms: x2 + -1(1 + x) = 21 x2 + (1 * -1 + x * -1) = 21 x2 + (-1 + -1x) = 21 Reorder the terms: -1 + -1x + x2 = 21 Solving -1 + -1x + x2 = 21 Solving for variable 'x'. Reorder the terms: -1 + -21 + -1x + x2 = 21 + -21 Combine like terms: -1 + -21 = -22 -22 + -1x + x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -22 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + -1x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + -1x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -1x + x2 = 0 + 22 -1x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 -1x + x2 = 22 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 22 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 22 + 0.25 Combine like terms: 22 + 0.25 = 22.25 0.25 + -1x + x2 = 22.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (x + -0.5) equal to 4.716990566 and -4.716990566.Subproblem 1
x + -0.5 = 4.716990566 Simplifying x + -0.5 = 4.716990566 Reorder the terms: -0.5 + x = 4.716990566 Solving -0.5 + x = 4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 4.716990566 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 4.716990566 + 0.5 x = 4.716990566 + 0.5 Combine like terms: 4.716990566 + 0.5 = 5.216990566 x = 5.216990566 Simplifying x = 5.216990566Subproblem 2
x + -0.5 = -4.716990566 Simplifying x + -0.5 = -4.716990566 Reorder the terms: -0.5 + x = -4.716990566 Solving -0.5 + x = -4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -4.716990566 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -4.716990566 + 0.5 x = -4.716990566 + 0.5 Combine like terms: -4.716990566 + 0.5 = -4.216990566 x = -4.216990566 Simplifying x = -4.216990566Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.216990566, -4.216990566}
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