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Simplifying 60 + -1x2 = x2 + 9x + 30 Reorder the terms: 60 + -1x2 = 30 + 9x + x2 Solving 60 + -1x2 = 30 + 9x + x2 Solving for variable 'x'. Reorder the terms: 60 + -30 + -9x + -1x2 + -1x2 = 30 + 9x + x2 + -30 + -9x + -1x2 Combine like terms: 60 + -30 = 30 30 + -9x + -1x2 + -1x2 = 30 + 9x + x2 + -30 + -9x + -1x2 Combine like terms: -1x2 + -1x2 = -2x2 30 + -9x + -2x2 = 30 + 9x + x2 + -30 + -9x + -1x2 Reorder the terms: 30 + -9x + -2x2 = 30 + -30 + 9x + -9x + x2 + -1x2 Combine like terms: 30 + -30 = 0 30 + -9x + -2x2 = 0 + 9x + -9x + x2 + -1x2 30 + -9x + -2x2 = 9x + -9x + x2 + -1x2 Combine like terms: 9x + -9x = 0 30 + -9x + -2x2 = 0 + x2 + -1x2 30 + -9x + -2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 30 + -9x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -15 + 4.5x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 4.5x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 4.5x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 4.5x + x2 = 0 + 15 4.5x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 4.5x + x2 = 15 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 15 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 15 + 5.0625 Combine like terms: 15 + 5.0625 = 20.0625 5.0625 + 4.5x + x2 = 20.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 20.0625 Calculate the square root of the right side: 4.479118217 Break this problem into two subproblems by setting (x + 2.25) equal to 4.479118217 and -4.479118217.Subproblem 1
x + 2.25 = 4.479118217 Simplifying x + 2.25 = 4.479118217 Reorder the terms: 2.25 + x = 4.479118217 Solving 2.25 + x = 4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 4.479118217 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 4.479118217 + -2.25 x = 4.479118217 + -2.25 Combine like terms: 4.479118217 + -2.25 = 2.229118217 x = 2.229118217 Simplifying x = 2.229118217Subproblem 2
x + 2.25 = -4.479118217 Simplifying x + 2.25 = -4.479118217 Reorder the terms: 2.25 + x = -4.479118217 Solving 2.25 + x = -4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -4.479118217 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -4.479118217 + -2.25 x = -4.479118217 + -2.25 Combine like terms: -4.479118217 + -2.25 = -6.729118217 x = -6.729118217 Simplifying x = -6.729118217Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.229118217, -6.729118217}
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