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Simplifying x2 + -10x + 18.75 = 0 Reorder the terms: 18.75 + -10x + x2 = 0 Solving 18.75 + -10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-18.75' to each side of the equation. 18.75 + -10x + -18.75 + x2 = 0 + -18.75 Reorder the terms: 18.75 + -18.75 + -10x + x2 = 0 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + -10x + x2 = 0 + -18.75 -10x + x2 = 0 + -18.75 Combine like terms: 0 + -18.75 = -18.75 -10x + x2 = -18.75 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 = -18.75 + 25 Reorder the terms: 25 + -10x + x2 = -18.75 + 25 Combine like terms: -18.75 + 25 = 6.25 25 + -10x + x2 = 6.25 Factor a perfect square on the left side: (x + -5)(x + -5) = 6.25 Calculate the square root of the right side: 2.5 Break this problem into two subproblems by setting (x + -5) equal to 2.5 and -2.5.Subproblem 1
x + -5 = 2.5 Simplifying x + -5 = 2.5 Reorder the terms: -5 + x = 2.5 Solving -5 + x = 2.5 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 = 2.5 + 5 Combine like terms: -5 + 5 = 0 0 + x = 2.5 + 5 x = 2.5 + 5 Combine like terms: 2.5 + 5 = 7.5 x = 7.5 Simplifying x = 7.5Subproblem 2
x + -5 = -2.5 Simplifying x + -5 = -2.5 Reorder the terms: -5 + x = -2.5 Solving -5 + x = -2.5 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 = -2.5 + 5 Combine like terms: -5 + 5 = 0 0 + x = -2.5 + 5 x = -2.5 + 5 Combine like terms: -2.5 + 5 = 2.5 x = 2.5 Simplifying x = 2.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.5, 2.5}
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