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Simplifying 0 = x2 + 10x + -60 Reorder the terms: 0 = -60 + 10x + x2 Solving 0 = -60 + 10x + x2 Solving for variable 'x'. Combine like terms: 0 + 60 = 60 60 + -10x + -1x2 = -60 + 10x + x2 + 60 + -10x + -1x2 Reorder the terms: 60 + -10x + -1x2 = -60 + 60 + 10x + -10x + x2 + -1x2 Combine like terms: -60 + 60 = 0 60 + -10x + -1x2 = 0 + 10x + -10x + x2 + -1x2 60 + -10x + -1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 60 + -10x + -1x2 = 0 + x2 + -1x2 60 + -10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 60 + -10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -60 + 10x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + 10x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 10x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 10x + x2 = 0 + 60 10x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 10x + x2 = 60 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 60 + 25 Reorder the terms: 25 + 10x + x2 = 60 + 25 Combine like terms: 60 + 25 = 85 25 + 10x + x2 = 85 Factor a perfect square on the left side: (x + 5)(x + 5) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (x + 5) equal to 9.219544457 and -9.219544457.Subproblem 1
x + 5 = 9.219544457 Simplifying x + 5 = 9.219544457 Reorder the terms: 5 + x = 9.219544457 Solving 5 + x = 9.219544457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 9.219544457 + -5 Combine like terms: 5 + -5 = 0 0 + x = 9.219544457 + -5 x = 9.219544457 + -5 Combine like terms: 9.219544457 + -5 = 4.219544457 x = 4.219544457 Simplifying x = 4.219544457Subproblem 2
x + 5 = -9.219544457 Simplifying x + 5 = -9.219544457 Reorder the terms: 5 + x = -9.219544457 Solving 5 + x = -9.219544457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -9.219544457 + -5 Combine like terms: 5 + -5 = 0 0 + x = -9.219544457 + -5 x = -9.219544457 + -5 Combine like terms: -9.219544457 + -5 = -14.219544457 x = -14.219544457 Simplifying x = -14.219544457Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.219544457, -14.219544457}
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