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Simplifying x2 + -8x + 13.56 = 0 Reorder the terms: 13.56 + -8x + x2 = 0 Solving 13.56 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-13.56' to each side of the equation. 13.56 + -8x + -13.56 + x2 = 0 + -13.56 Reorder the terms: 13.56 + -13.56 + -8x + x2 = 0 + -13.56 Combine like terms: 13.56 + -13.56 = 0.00 0.00 + -8x + x2 = 0 + -13.56 -8x + x2 = 0 + -13.56 Combine like terms: 0 + -13.56 = -13.56 -8x + x2 = -13.56 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 = -13.56 + 16 Reorder the terms: 16 + -8x + x2 = -13.56 + 16 Combine like terms: -13.56 + 16 = 2.44 16 + -8x + x2 = 2.44 Factor a perfect square on the left side: (x + -4)(x + -4) = 2.44 Calculate the square root of the right side: 1.562049935 Break this problem into two subproblems by setting (x + -4) equal to 1.562049935 and -1.562049935.Subproblem 1
x + -4 = 1.562049935 Simplifying x + -4 = 1.562049935 Reorder the terms: -4 + x = 1.562049935 Solving -4 + x = 1.562049935 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 = 1.562049935 + 4 Combine like terms: -4 + 4 = 0 0 + x = 1.562049935 + 4 x = 1.562049935 + 4 Combine like terms: 1.562049935 + 4 = 5.562049935 x = 5.562049935 Simplifying x = 5.562049935Subproblem 2
x + -4 = -1.562049935 Simplifying x + -4 = -1.562049935 Reorder the terms: -4 + x = -1.562049935 Solving -4 + x = -1.562049935 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 = -1.562049935 + 4 Combine like terms: -4 + 4 = 0 0 + x = -1.562049935 + 4 x = -1.562049935 + 4 Combine like terms: -1.562049935 + 4 = 2.437950065 x = 2.437950065 Simplifying x = 2.437950065Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.562049935, 2.437950065}
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