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Simplifying x2 + -8x + 15.75 = 0 Reorder the terms: 15.75 + -8x + x2 = 0 Solving 15.75 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-15.75' to each side of the equation. 15.75 + -8x + -15.75 + x2 = 0 + -15.75 Reorder the terms: 15.75 + -15.75 + -8x + x2 = 0 + -15.75 Combine like terms: 15.75 + -15.75 = 0.00 0.00 + -8x + x2 = 0 + -15.75 -8x + x2 = 0 + -15.75 Combine like terms: 0 + -15.75 = -15.75 -8x + x2 = -15.75 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 = -15.75 + 16 Reorder the terms: 16 + -8x + x2 = -15.75 + 16 Combine like terms: -15.75 + 16 = 0.25 16 + -8x + x2 = 0.25 Factor a perfect square on the left side: (x + -4)(x + -4) = 0.25 Calculate the square root of the right side: 0.5 Break this problem into two subproblems by setting (x + -4) equal to 0.5 and -0.5.Subproblem 1
x + -4 = 0.5 Simplifying x + -4 = 0.5 Reorder the terms: -4 + x = 0.5 Solving -4 + x = 0.5 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 = 0.5 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0.5 + 4 x = 0.5 + 4 Combine like terms: 0.5 + 4 = 4.5 x = 4.5 Simplifying x = 4.5Subproblem 2
x + -4 = -0.5 Simplifying x + -4 = -0.5 Reorder the terms: -4 + x = -0.5 Solving -4 + x = -0.5 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 = -0.5 + 4 Combine like terms: -4 + 4 = 0 0 + x = -0.5 + 4 x = -0.5 + 4 Combine like terms: -0.5 + 4 = 3.5 x = 3.5 Simplifying x = 3.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.5, 3.5}
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