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Simplifying x2 + -8x + -23 = 5 Reorder the terms: -23 + -8x + x2 = 5 Solving -23 + -8x + x2 = 5 Solving for variable 'x'. Reorder the terms: -23 + -5 + -8x + x2 = 5 + -5 Combine like terms: -23 + -5 = -28 -28 + -8x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -28 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -8x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -8x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -8x + x2 = 0 + 28 -8x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -8x + x2 = 28 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 = 28 + 16 Reorder the terms: 16 + -8x + x2 = 28 + 16 Combine like terms: 28 + 16 = 44 16 + -8x + x2 = 44 Factor a perfect square on the left side: (x + -4)(x + -4) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (x + -4) equal to 6.633249581 and -6.633249581.Subproblem 1
x + -4 = 6.633249581 Simplifying x + -4 = 6.633249581 Reorder the terms: -4 + x = 6.633249581 Solving -4 + x = 6.633249581 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 = 6.633249581 + 4 Combine like terms: -4 + 4 = 0 0 + x = 6.633249581 + 4 x = 6.633249581 + 4 Combine like terms: 6.633249581 + 4 = 10.633249581 x = 10.633249581 Simplifying x = 10.633249581Subproblem 2
x + -4 = -6.633249581 Simplifying x + -4 = -6.633249581 Reorder the terms: -4 + x = -6.633249581 Solving -4 + x = -6.633249581 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 = -6.633249581 + 4 Combine like terms: -4 + 4 = 0 0 + x = -6.633249581 + 4 x = -6.633249581 + 4 Combine like terms: -6.633249581 + 4 = -2.633249581 x = -2.633249581 Simplifying x = -2.633249581Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.633249581, -2.633249581}
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