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Simplifying x2 + -8x + -20 = 69 Reorder the terms: -20 + -8x + x2 = 69 Solving -20 + -8x + x2 = 69 Solving for variable 'x'. Reorder the terms: -20 + -69 + -8x + x2 = 69 + -69 Combine like terms: -20 + -69 = -89 -89 + -8x + x2 = 69 + -69 Combine like terms: 69 + -69 = 0 -89 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '89' to each side of the equation. -89 + -8x + 89 + x2 = 0 + 89 Reorder the terms: -89 + 89 + -8x + x2 = 0 + 89 Combine like terms: -89 + 89 = 0 0 + -8x + x2 = 0 + 89 -8x + x2 = 0 + 89 Combine like terms: 0 + 89 = 89 -8x + x2 = 89 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 = 89 + 16 Reorder the terms: 16 + -8x + x2 = 89 + 16 Combine like terms: 89 + 16 = 105 16 + -8x + x2 = 105 Factor a perfect square on the left side: (x + -4)(x + -4) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (x + -4) equal to 10.246950766 and -10.246950766.Subproblem 1
x + -4 = 10.246950766 Simplifying x + -4 = 10.246950766 Reorder the terms: -4 + x = 10.246950766 Solving -4 + x = 10.246950766 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 = 10.246950766 + 4 Combine like terms: -4 + 4 = 0 0 + x = 10.246950766 + 4 x = 10.246950766 + 4 Combine like terms: 10.246950766 + 4 = 14.246950766 x = 14.246950766 Simplifying x = 14.246950766Subproblem 2
x + -4 = -10.246950766 Simplifying x + -4 = -10.246950766 Reorder the terms: -4 + x = -10.246950766 Solving -4 + x = -10.246950766 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 = -10.246950766 + 4 Combine like terms: -4 + 4 = 0 0 + x = -10.246950766 + 4 x = -10.246950766 + 4 Combine like terms: -10.246950766 + 4 = -6.246950766 x = -6.246950766 Simplifying x = -6.246950766Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.246950766, -6.246950766}
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