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Simplifying x2 + -8x + -24 = 20 Reorder the terms: -24 + -8x + x2 = 20 Solving -24 + -8x + x2 = 20 Solving for variable 'x'. Reorder the terms: -24 + -20 + -8x + x2 = 20 + -20 Combine like terms: -24 + -20 = -44 -44 + -8x + x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -44 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + -8x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + -8x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -8x + x2 = 0 + 44 -8x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 -8x + x2 = 44 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 = 44 + 16 Reorder the terms: 16 + -8x + x2 = 44 + 16 Combine like terms: 44 + 16 = 60 16 + -8x + x2 = 60 Factor a perfect square on the left side: (x + -4)(x + -4) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + -4) equal to 7.745966692 and -7.745966692.Subproblem 1
x + -4 = 7.745966692 Simplifying x + -4 = 7.745966692 Reorder the terms: -4 + x = 7.745966692 Solving -4 + x = 7.745966692 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 = 7.745966692 + 4 Combine like terms: -4 + 4 = 0 0 + x = 7.745966692 + 4 x = 7.745966692 + 4 Combine like terms: 7.745966692 + 4 = 11.745966692 x = 11.745966692 Simplifying x = 11.745966692Subproblem 2
x + -4 = -7.745966692 Simplifying x + -4 = -7.745966692 Reorder the terms: -4 + x = -7.745966692 Solving -4 + x = -7.745966692 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 = -7.745966692 + 4 Combine like terms: -4 + 4 = 0 0 + x = -7.745966692 + 4 x = -7.745966692 + 4 Combine like terms: -7.745966692 + 4 = -3.745966692 x = -3.745966692 Simplifying x = -3.745966692Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.745966692, -3.745966692}
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