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Simplifying 2x + 261 = x2 Reorder the terms: 261 + 2x = x2 Solving 261 + 2x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 261 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -261 + -2x + x2 = 0 Move the constant term to the right: Add '261' to each side of the equation. -261 + -2x + 261 + x2 = 0 + 261 Reorder the terms: -261 + 261 + -2x + x2 = 0 + 261 Combine like terms: -261 + 261 = 0 0 + -2x + x2 = 0 + 261 -2x + x2 = 0 + 261 Combine like terms: 0 + 261 = 261 -2x + x2 = 261 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 261 + 1 Reorder the terms: 1 + -2x + x2 = 261 + 1 Combine like terms: 261 + 1 = 262 1 + -2x + x2 = 262 Factor a perfect square on the left side: (x + -1)(x + -1) = 262 Calculate the square root of the right side: 16.186414056 Break this problem into two subproblems by setting (x + -1) equal to 16.186414056 and -16.186414056.Subproblem 1
x + -1 = 16.186414056 Simplifying x + -1 = 16.186414056 Reorder the terms: -1 + x = 16.186414056 Solving -1 + x = 16.186414056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 16.186414056 + 1 Combine like terms: -1 + 1 = 0 0 + x = 16.186414056 + 1 x = 16.186414056 + 1 Combine like terms: 16.186414056 + 1 = 17.186414056 x = 17.186414056 Simplifying x = 17.186414056Subproblem 2
x + -1 = -16.186414056 Simplifying x + -1 = -16.186414056 Reorder the terms: -1 + x = -16.186414056 Solving -1 + x = -16.186414056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -16.186414056 + 1 Combine like terms: -1 + 1 = 0 0 + x = -16.186414056 + 1 x = -16.186414056 + 1 Combine like terms: -16.186414056 + 1 = -15.186414056 x = -15.186414056 Simplifying x = -15.186414056Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.186414056, -15.186414056}
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