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Simplifying x2 + -35x + 225 = 0 Reorder the terms: 225 + -35x + x2 = 0 Solving 225 + -35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-225' to each side of the equation. 225 + -35x + -225 + x2 = 0 + -225 Reorder the terms: 225 + -225 + -35x + x2 = 0 + -225 Combine like terms: 225 + -225 = 0 0 + -35x + x2 = 0 + -225 -35x + x2 = 0 + -225 Combine like terms: 0 + -225 = -225 -35x + x2 = -225 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 = -225 + 306.25 Reorder the terms: 306.25 + -35x + x2 = -225 + 306.25 Combine like terms: -225 + 306.25 = 81.25 306.25 + -35x + x2 = 81.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 81.25 Calculate the square root of the right side: 9.013878189 Break this problem into two subproblems by setting (x + -17.5) equal to 9.013878189 and -9.013878189.Subproblem 1
x + -17.5 = 9.013878189 Simplifying x + -17.5 = 9.013878189 Reorder the terms: -17.5 + x = 9.013878189 Solving -17.5 + x = 9.013878189 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 = 9.013878189 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 9.013878189 + 17.5 x = 9.013878189 + 17.5 Combine like terms: 9.013878189 + 17.5 = 26.513878189 x = 26.513878189 Simplifying x = 26.513878189Subproblem 2
x + -17.5 = -9.013878189 Simplifying x + -17.5 = -9.013878189 Reorder the terms: -17.5 + x = -9.013878189 Solving -17.5 + x = -9.013878189 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 = -9.013878189 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -9.013878189 + 17.5 x = -9.013878189 + 17.5 Combine like terms: -9.013878189 + 17.5 = 8.486121811 x = 8.486121811 Simplifying x = 8.486121811Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.513878189, 8.486121811}
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