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Simplifying 0 = x2 + 4x + -560 Reorder the terms: 0 = -560 + 4x + x2 Solving 0 = -560 + 4x + x2 Solving for variable 'x'. Combine like terms: 0 + 560 = 560 560 + -4x + -1x2 = -560 + 4x + x2 + 560 + -4x + -1x2 Reorder the terms: 560 + -4x + -1x2 = -560 + 560 + 4x + -4x + x2 + -1x2 Combine like terms: -560 + 560 = 0 560 + -4x + -1x2 = 0 + 4x + -4x + x2 + -1x2 560 + -4x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 560 + -4x + -1x2 = 0 + x2 + -1x2 560 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 560 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -560 + 4x + x2 = 0 Move the constant term to the right: Add '560' to each side of the equation. -560 + 4x + 560 + x2 = 0 + 560 Reorder the terms: -560 + 560 + 4x + x2 = 0 + 560 Combine like terms: -560 + 560 = 0 0 + 4x + x2 = 0 + 560 4x + x2 = 0 + 560 Combine like terms: 0 + 560 = 560 4x + x2 = 560 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 560 + 4 Reorder the terms: 4 + 4x + x2 = 560 + 4 Combine like terms: 560 + 4 = 564 4 + 4x + x2 = 564 Factor a perfect square on the left side: (x + 2)(x + 2) = 564 Calculate the square root of the right side: 23.748684174 Break this problem into two subproblems by setting (x + 2) equal to 23.748684174 and -23.748684174.Subproblem 1
x + 2 = 23.748684174 Simplifying x + 2 = 23.748684174 Reorder the terms: 2 + x = 23.748684174 Solving 2 + x = 23.748684174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 23.748684174 + -2 Combine like terms: 2 + -2 = 0 0 + x = 23.748684174 + -2 x = 23.748684174 + -2 Combine like terms: 23.748684174 + -2 = 21.748684174 x = 21.748684174 Simplifying x = 21.748684174Subproblem 2
x + 2 = -23.748684174 Simplifying x + 2 = -23.748684174 Reorder the terms: 2 + x = -23.748684174 Solving 2 + x = -23.748684174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -23.748684174 + -2 Combine like terms: 2 + -2 = 0 0 + x = -23.748684174 + -2 x = -23.748684174 + -2 Combine like terms: -23.748684174 + -2 = -25.748684174 x = -25.748684174 Simplifying x = -25.748684174Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.748684174, -25.748684174}
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