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Simplifying 45x + -1x2 + -6 = 0 Reorder the terms: -6 + 45x + -1x2 = 0 Solving -6 + 45x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 6 + -45x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -45x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -45x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -45x + x2 = 0 + -6 -45x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -45x + x2 = -6 The x term is -45x. Take half its coefficient (-22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. -45x + 506.25 + x2 = -6 + 506.25 Reorder the terms: 506.25 + -45x + x2 = -6 + 506.25 Combine like terms: -6 + 506.25 = 500.25 506.25 + -45x + x2 = 500.25 Factor a perfect square on the left side: (x + -22.5)(x + -22.5) = 500.25 Calculate the square root of the right side: 22.366269246 Break this problem into two subproblems by setting (x + -22.5) equal to 22.366269246 and -22.366269246.Subproblem 1
x + -22.5 = 22.366269246 Simplifying x + -22.5 = 22.366269246 Reorder the terms: -22.5 + x = 22.366269246 Solving -22.5 + x = 22.366269246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = 22.366269246 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 22.366269246 + 22.5 x = 22.366269246 + 22.5 Combine like terms: 22.366269246 + 22.5 = 44.866269246 x = 44.866269246 Simplifying x = 44.866269246Subproblem 2
x + -22.5 = -22.366269246 Simplifying x + -22.5 = -22.366269246 Reorder the terms: -22.5 + x = -22.366269246 Solving -22.5 + x = -22.366269246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = -22.366269246 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -22.366269246 + 22.5 x = -22.366269246 + 22.5 Combine like terms: -22.366269246 + 22.5 = 0.133730754 x = 0.133730754 Simplifying x = 0.133730754Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.866269246, 0.133730754}
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