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Simplifying x2 + -30x + 209.375 = 0 Reorder the terms: 209.375 + -30x + x2 = 0 Solving 209.375 + -30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-209.375' to each side of the equation. 209.375 + -30x + -209.375 + x2 = 0 + -209.375 Reorder the terms: 209.375 + -209.375 + -30x + x2 = 0 + -209.375 Combine like terms: 209.375 + -209.375 = 0.000 0.000 + -30x + x2 = 0 + -209.375 -30x + x2 = 0 + -209.375 Combine like terms: 0 + -209.375 = -209.375 -30x + x2 = -209.375 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -209.375 + 225 Reorder the terms: 225 + -30x + x2 = -209.375 + 225 Combine like terms: -209.375 + 225 = 15.625 225 + -30x + x2 = 15.625 Factor a perfect square on the left side: (x + -15)(x + -15) = 15.625 Calculate the square root of the right side: 3.952847075 Break this problem into two subproblems by setting (x + -15) equal to 3.952847075 and -3.952847075.Subproblem 1
x + -15 = 3.952847075 Simplifying x + -15 = 3.952847075 Reorder the terms: -15 + x = 3.952847075 Solving -15 + x = 3.952847075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 3.952847075 + 15 Combine like terms: -15 + 15 = 0 0 + x = 3.952847075 + 15 x = 3.952847075 + 15 Combine like terms: 3.952847075 + 15 = 18.952847075 x = 18.952847075 Simplifying x = 18.952847075Subproblem 2
x + -15 = -3.952847075 Simplifying x + -15 = -3.952847075 Reorder the terms: -15 + x = -3.952847075 Solving -15 + x = -3.952847075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -3.952847075 + 15 Combine like terms: -15 + 15 = 0 0 + x = -3.952847075 + 15 x = -3.952847075 + 15 Combine like terms: -3.952847075 + 15 = 11.047152925 x = 11.047152925 Simplifying x = 11.047152925Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.952847075, 11.047152925}
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