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Simplifying 0 = x(x + 2) + -2304 Reorder the terms: 0 = x(2 + x) + -2304 0 = (2 * x + x * x) + -2304 0 = (2x + x2) + -2304 Reorder the terms: 0 = -2304 + 2x + x2 Solving 0 = -2304 + 2x + x2 Solving for variable 'x'. Combine like terms: 0 + 2304 = 2304 2304 + -2x + -1x2 = -2304 + 2x + x2 + 2304 + -2x + -1x2 Reorder the terms: 2304 + -2x + -1x2 = -2304 + 2304 + 2x + -2x + x2 + -1x2 Combine like terms: -2304 + 2304 = 0 2304 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2 2304 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 2304 + -2x + -1x2 = 0 + x2 + -1x2 2304 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 2304 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2304 + 2x + x2 = 0 Move the constant term to the right: Add '2304' to each side of the equation. -2304 + 2x + 2304 + x2 = 0 + 2304 Reorder the terms: -2304 + 2304 + 2x + x2 = 0 + 2304 Combine like terms: -2304 + 2304 = 0 0 + 2x + x2 = 0 + 2304 2x + x2 = 0 + 2304 Combine like terms: 0 + 2304 = 2304 2x + x2 = 2304 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 = 2304 + 1 Reorder the terms: 1 + 2x + x2 = 2304 + 1 Combine like terms: 2304 + 1 = 2305 1 + 2x + x2 = 2305 Factor a perfect square on the left side: (x + 1)(x + 1) = 2305 Calculate the square root of the right side: 48.010415537 Break this problem into two subproblems by setting (x + 1) equal to 48.010415537 and -48.010415537.Subproblem 1
x + 1 = 48.010415537 Simplifying x + 1 = 48.010415537 Reorder the terms: 1 + x = 48.010415537 Solving 1 + x = 48.010415537 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 = 48.010415537 + -1 Combine like terms: 1 + -1 = 0 0 + x = 48.010415537 + -1 x = 48.010415537 + -1 Combine like terms: 48.010415537 + -1 = 47.010415537 x = 47.010415537 Simplifying x = 47.010415537Subproblem 2
x + 1 = -48.010415537 Simplifying x + 1 = -48.010415537 Reorder the terms: 1 + x = -48.010415537 Solving 1 + x = -48.010415537 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 = -48.010415537 + -1 Combine like terms: 1 + -1 = 0 0 + x = -48.010415537 + -1 x = -48.010415537 + -1 Combine like terms: -48.010415537 + -1 = -49.010415537 x = -49.010415537 Simplifying x = -49.010415537Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.010415537, -49.010415537}
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