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Simplifying x2 + -35x + 306.25 = 0 Reorder the terms: 306.25 + -35x + x2 = 0 Solving 306.25 + -35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-306.25' to each side of the equation. 306.25 + -35x + -306.25 + x2 = 0 + -306.25 Reorder the terms: 306.25 + -306.25 + -35x + x2 = 0 + -306.25 Combine like terms: 306.25 + -306.25 = 0.00 0.00 + -35x + x2 = 0 + -306.25 -35x + x2 = 0 + -306.25 Combine like terms: 0 + -306.25 = -306.25 -35x + x2 = -306.25 The x term is -35x. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35x + 306.25 + x2 = -306.25 + 306.25 Reorder the terms: 306.25 + -35x + x2 = -306.25 + 306.25 Combine like terms: -306.25 + 306.25 = 0.00 306.25 + -35x + x2 = 0.00 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + -17.5) equal to 0.00 and 0.00.Subproblem 1
x + -17.5 = 0.00 Simplifying x + -17.5 = 0.00 Reorder the terms: -17.5 + x = 0.00 Solving -17.5 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = 0.00 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 0.00 + 17.5 x = 0.00 + 17.5 Combine like terms: 0.00 + 17.5 = 17.5 x = 17.5 Simplifying x = 17.5Subproblem 2
x + -17.5 = 0.00 Simplifying x + -17.5 = 0.00 Reorder the terms: -17.5 + x = 0.00 Solving -17.5 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = 0.00 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 0.00 + 17.5 x = 0.00 + 17.5 Combine like terms: 0.00 + 17.5 = 17.5 x = 17.5 Simplifying x = 17.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.5, 17.5}
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