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Simplifying x2 + -30x = 2 Reorder the terms: -30x + x2 = 2 Solving -30x + x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + -30x + x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -30x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -30x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -30x + x2 = 0 + 2 -30x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -30x + x2 = 2 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 = 2 + 225 Reorder the terms: 225 + -30x + x2 = 2 + 225 Combine like terms: 2 + 225 = 227 225 + -30x + x2 = 227 Factor a perfect square on the left side: (x + -15)(x + -15) = 227 Calculate the square root of the right side: 15.066519173 Break this problem into two subproblems by setting (x + -15) equal to 15.066519173 and -15.066519173.Subproblem 1
x + -15 = 15.066519173 Simplifying x + -15 = 15.066519173 Reorder the terms: -15 + x = 15.066519173 Solving -15 + x = 15.066519173 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 = 15.066519173 + 15 Combine like terms: -15 + 15 = 0 0 + x = 15.066519173 + 15 x = 15.066519173 + 15 Combine like terms: 15.066519173 + 15 = 30.066519173 x = 30.066519173 Simplifying x = 30.066519173Subproblem 2
x + -15 = -15.066519173 Simplifying x + -15 = -15.066519173 Reorder the terms: -15 + x = -15.066519173 Solving -15 + x = -15.066519173 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 = -15.066519173 + 15 Combine like terms: -15 + 15 = 0 0 + x = -15.066519173 + 15 x = -15.066519173 + 15 Combine like terms: -15.066519173 + 15 = -0.066519173 x = -0.066519173 Simplifying x = -0.066519173Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.066519173, -0.066519173}
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