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Simplifying x2 + -10x + 12.75 = 0 Reorder the terms: 12.75 + -10x + x2 = 0 Solving 12.75 + -10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-12.75' to each side of the equation. 12.75 + -10x + -12.75 + x2 = 0 + -12.75 Reorder the terms: 12.75 + -12.75 + -10x + x2 = 0 + -12.75 Combine like terms: 12.75 + -12.75 = 0.00 0.00 + -10x + x2 = 0 + -12.75 -10x + x2 = 0 + -12.75 Combine like terms: 0 + -12.75 = -12.75 -10x + x2 = -12.75 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -12.75 + 25 Reorder the terms: 25 + -10x + x2 = -12.75 + 25 Combine like terms: -12.75 + 25 = 12.25 25 + -10x + x2 = 12.25 Factor a perfect square on the left side: (x + -5)(x + -5) = 12.25 Calculate the square root of the right side: 3.5 Break this problem into two subproblems by setting (x + -5) equal to 3.5 and -3.5.Subproblem 1
x + -5 = 3.5 Simplifying x + -5 = 3.5 Reorder the terms: -5 + x = 3.5 Solving -5 + x = 3.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 3.5 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.5 + 5 x = 3.5 + 5 Combine like terms: 3.5 + 5 = 8.5 x = 8.5 Simplifying x = 8.5Subproblem 2
x + -5 = -3.5 Simplifying x + -5 = -3.5 Reorder the terms: -5 + x = -3.5 Solving -5 + x = -3.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -3.5 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.5 + 5 x = -3.5 + 5 Combine like terms: -3.5 + 5 = 1.5 x = 1.5 Simplifying x = 1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.5, 1.5}
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