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Simplifying x2 + -8x + 13.75 = 0 Reorder the terms: 13.75 + -8x + x2 = 0 Solving 13.75 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-13.75' to each side of the equation. 13.75 + -8x + -13.75 + x2 = 0 + -13.75 Reorder the terms: 13.75 + -13.75 + -8x + x2 = 0 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + -8x + x2 = 0 + -13.75 -8x + x2 = 0 + -13.75 Combine like terms: 0 + -13.75 = -13.75 -8x + x2 = -13.75 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 = -13.75 + 16 Reorder the terms: 16 + -8x + x2 = -13.75 + 16 Combine like terms: -13.75 + 16 = 2.25 16 + -8x + x2 = 2.25 Factor a perfect square on the left side: (x + -4)(x + -4) = 2.25 Calculate the square root of the right side: 1.5 Break this problem into two subproblems by setting (x + -4) equal to 1.5 and -1.5.Subproblem 1
x + -4 = 1.5 Simplifying x + -4 = 1.5 Reorder the terms: -4 + x = 1.5 Solving -4 + x = 1.5 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 = 1.5 + 4 Combine like terms: -4 + 4 = 0 0 + x = 1.5 + 4 x = 1.5 + 4 Combine like terms: 1.5 + 4 = 5.5 x = 5.5 Simplifying x = 5.5Subproblem 2
x + -4 = -1.5 Simplifying x + -4 = -1.5 Reorder the terms: -4 + x = -1.5 Solving -4 + x = -1.5 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 = -1.5 + 4 Combine like terms: -4 + 4 = 0 0 + x = -1.5 + 4 x = -1.5 + 4 Combine like terms: -1.5 + 4 = 2.5 x = 2.5 Simplifying x = 2.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.5, 2.5}
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