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Simplifying -5x = x2 + 3x + -21 Reorder the terms: -5x = -21 + 3x + x2 Solving -5x = -21 + 3x + x2 Solving for variable 'x'. Reorder the terms: 21 + -5x + -3x + -1x2 = -21 + 3x + x2 + 21 + -3x + -1x2 Combine like terms: -5x + -3x = -8x 21 + -8x + -1x2 = -21 + 3x + x2 + 21 + -3x + -1x2 Reorder the terms: 21 + -8x + -1x2 = -21 + 21 + 3x + -3x + x2 + -1x2 Combine like terms: -21 + 21 = 0 21 + -8x + -1x2 = 0 + 3x + -3x + x2 + -1x2 21 + -8x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 21 + -8x + -1x2 = 0 + x2 + -1x2 21 + -8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 21 + -8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -21 + 8x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + 8x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 8x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 8x + x2 = 0 + 21 8x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 8x + x2 = 21 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 21 + 16 Reorder the terms: 16 + 8x + x2 = 21 + 16 Combine like terms: 21 + 16 = 37 16 + 8x + x2 = 37 Factor a perfect square on the left side: (x + 4)(x + 4) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (x + 4) equal to 6.08276253 and -6.08276253.Subproblem 1
x + 4 = 6.08276253 Simplifying x + 4 = 6.08276253 Reorder the terms: 4 + x = 6.08276253 Solving 4 + x = 6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 6.08276253 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.08276253 + -4 x = 6.08276253 + -4 Combine like terms: 6.08276253 + -4 = 2.08276253 x = 2.08276253 Simplifying x = 2.08276253Subproblem 2
x + 4 = -6.08276253 Simplifying x + 4 = -6.08276253 Reorder the terms: 4 + x = -6.08276253 Solving 4 + x = -6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -6.08276253 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.08276253 + -4 x = -6.08276253 + -4 Combine like terms: -6.08276253 + -4 = -10.08276253 x = -10.08276253 Simplifying x = -10.08276253Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.08276253, -10.08276253}
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