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Simplifying x2 + -30x = 35 Reorder the terms: -30x + x2 = 35 Solving -30x + x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + -30x + x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -30x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + -30x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -30x + x2 = 0 + 35 -30x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 -30x + x2 = 35 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 = 35 + 225 Reorder the terms: 225 + -30x + x2 = 35 + 225 Combine like terms: 35 + 225 = 260 225 + -30x + x2 = 260 Factor a perfect square on the left side: (x + -15)(x + -15) = 260 Calculate the square root of the right side: 16.124515497 Break this problem into two subproblems by setting (x + -15) equal to 16.124515497 and -16.124515497.Subproblem 1
x + -15 = 16.124515497 Simplifying x + -15 = 16.124515497 Reorder the terms: -15 + x = 16.124515497 Solving -15 + x = 16.124515497 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 = 16.124515497 + 15 Combine like terms: -15 + 15 = 0 0 + x = 16.124515497 + 15 x = 16.124515497 + 15 Combine like terms: 16.124515497 + 15 = 31.124515497 x = 31.124515497 Simplifying x = 31.124515497Subproblem 2
x + -15 = -16.124515497 Simplifying x + -15 = -16.124515497 Reorder the terms: -15 + x = -16.124515497 Solving -15 + x = -16.124515497 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 = -16.124515497 + 15 Combine like terms: -15 + 15 = 0 0 + x = -16.124515497 + 15 x = -16.124515497 + 15 Combine like terms: -16.124515497 + 15 = -1.124515497 x = -1.124515497 Simplifying x = -1.124515497Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.124515497, -1.124515497}
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