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Simplifying x2 + -30x = -1 Reorder the terms: -30x + x2 = -1 Solving -30x + x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + -30x + x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -30x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -30x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -30x + x2 = 0 + -1 -30x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -30x + x2 = -1 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 = -1 + 225 Reorder the terms: 225 + -30x + x2 = -1 + 225 Combine like terms: -1 + 225 = 224 225 + -30x + x2 = 224 Factor a perfect square on the left side: (x + -15)(x + -15) = 224 Calculate the square root of the right side: 14.966629547 Break this problem into two subproblems by setting (x + -15) equal to 14.966629547 and -14.966629547.Subproblem 1
x + -15 = 14.966629547 Simplifying x + -15 = 14.966629547 Reorder the terms: -15 + x = 14.966629547 Solving -15 + x = 14.966629547 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 = 14.966629547 + 15 Combine like terms: -15 + 15 = 0 0 + x = 14.966629547 + 15 x = 14.966629547 + 15 Combine like terms: 14.966629547 + 15 = 29.966629547 x = 29.966629547 Simplifying x = 29.966629547Subproblem 2
x + -15 = -14.966629547 Simplifying x + -15 = -14.966629547 Reorder the terms: -15 + x = -14.966629547 Solving -15 + x = -14.966629547 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 = -14.966629547 + 15 Combine like terms: -15 + 15 = 0 0 + x = -14.966629547 + 15 x = -14.966629547 + 15 Combine like terms: -14.966629547 + 15 = 0.033370453 x = 0.033370453 Simplifying x = 0.033370453Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.966629547, 0.033370453}
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