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Simplifying x2 + 8x + -20 = 20 Reorder the terms: -20 + 8x + x2 = 20 Solving -20 + 8x + x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + -20 + 8x + x2 = 20 + -20 Combine like terms: -20 + -20 = -40 -40 + 8x + x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -40 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 8x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 8x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 8x + x2 = 0 + 40 8x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 8x + x2 = 40 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 = 40 + 16 Reorder the terms: 16 + 8x + x2 = 40 + 16 Combine like terms: 40 + 16 = 56 16 + 8x + x2 = 56 Factor a perfect square on the left side: (x + 4)(x + 4) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (x + 4) equal to 7.483314774 and -7.483314774.Subproblem 1
x + 4 = 7.483314774 Simplifying x + 4 = 7.483314774 Reorder the terms: 4 + x = 7.483314774 Solving 4 + x = 7.483314774 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 = 7.483314774 + -4 Combine like terms: 4 + -4 = 0 0 + x = 7.483314774 + -4 x = 7.483314774 + -4 Combine like terms: 7.483314774 + -4 = 3.483314774 x = 3.483314774 Simplifying x = 3.483314774Subproblem 2
x + 4 = -7.483314774 Simplifying x + 4 = -7.483314774 Reorder the terms: 4 + x = -7.483314774 Solving 4 + x = -7.483314774 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 = -7.483314774 + -4 Combine like terms: 4 + -4 = 0 0 + x = -7.483314774 + -4 x = -7.483314774 + -4 Combine like terms: -7.483314774 + -4 = -11.483314774 x = -11.483314774 Simplifying x = -11.483314774Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.483314774, -11.483314774}
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