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Simplifying 4.5 = x2 + -9x + 8 Reorder the terms: 4.5 = 8 + -9x + x2 Solving 4.5 = 8 + -9x + x2 Solving for variable 'x'. Combine like terms: 4.5 + -8 = -3.5 -3.5 + 9x + -1x2 = 8 + -9x + x2 + -8 + 9x + -1x2 Reorder the terms: -3.5 + 9x + -1x2 = 8 + -8 + -9x + 9x + x2 + -1x2 Combine like terms: 8 + -8 = 0 -3.5 + 9x + -1x2 = 0 + -9x + 9x + x2 + -1x2 -3.5 + 9x + -1x2 = -9x + 9x + x2 + -1x2 Combine like terms: -9x + 9x = 0 -3.5 + 9x + -1x2 = 0 + x2 + -1x2 -3.5 + 9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -3.5 + 9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3.5 + -9x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -9x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -9x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -9x + x2 = 0 + -3.5 -9x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -9x + x2 = -3.5 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -3.5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -3.5 + 20.25 Combine like terms: -3.5 + 20.25 = 16.75 20.25 + -9x + x2 = 16.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 16.75 Calculate the square root of the right side: 4.092676386 Break this problem into two subproblems by setting (x + -4.5) equal to 4.092676386 and -4.092676386.Subproblem 1
x + -4.5 = 4.092676386 Simplifying x + -4.5 = 4.092676386 Reorder the terms: -4.5 + x = 4.092676386 Solving -4.5 + x = 4.092676386 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 4.092676386 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.092676386 + 4.5 x = 4.092676386 + 4.5 Combine like terms: 4.092676386 + 4.5 = 8.592676386 x = 8.592676386 Simplifying x = 8.592676386Subproblem 2
x + -4.5 = -4.092676386 Simplifying x + -4.5 = -4.092676386 Reorder the terms: -4.5 + x = -4.092676386 Solving -4.5 + x = -4.092676386 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -4.092676386 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.092676386 + 4.5 x = -4.092676386 + 4.5 Combine like terms: -4.092676386 + 4.5 = 0.407323614 x = 0.407323614 Simplifying x = 0.407323614Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.592676386, 0.407323614}
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