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Simplifying x2 + 8x + -20 = 6 Reorder the terms: -20 + 8x + x2 = 6 Solving -20 + 8x + x2 = 6 Solving for variable 'x'. Reorder the terms: -20 + -6 + 8x + x2 = 6 + -6 Combine like terms: -20 + -6 = -26 -26 + 8x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -26 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + 8x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + 8x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 8x + x2 = 0 + 26 8x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 8x + x2 = 26 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 = 26 + 16 Reorder the terms: 16 + 8x + x2 = 26 + 16 Combine like terms: 26 + 16 = 42 16 + 8x + x2 = 42 Factor a perfect square on the left side: (x + 4)(x + 4) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (x + 4) equal to 6.480740698 and -6.480740698.Subproblem 1
x + 4 = 6.480740698 Simplifying x + 4 = 6.480740698 Reorder the terms: 4 + x = 6.480740698 Solving 4 + x = 6.480740698 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 = 6.480740698 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.480740698 + -4 x = 6.480740698 + -4 Combine like terms: 6.480740698 + -4 = 2.480740698 x = 2.480740698 Simplifying x = 2.480740698Subproblem 2
x + 4 = -6.480740698 Simplifying x + 4 = -6.480740698 Reorder the terms: 4 + x = -6.480740698 Solving 4 + x = -6.480740698 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 = -6.480740698 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.480740698 + -4 x = -6.480740698 + -4 Combine like terms: -6.480740698 + -4 = -10.480740698 x = -10.480740698 Simplifying x = -10.480740698Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.480740698, -10.480740698}
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