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Simplifying 9x + 67 = x2 + 5 Reorder the terms: 67 + 9x = x2 + 5 Reorder the terms: 67 + 9x = 5 + x2 Solving 67 + 9x = 5 + x2 Solving for variable 'x'. Reorder the terms: 67 + -5 + 9x + -1x2 = 5 + x2 + -5 + -1x2 Combine like terms: 67 + -5 = 62 62 + 9x + -1x2 = 5 + x2 + -5 + -1x2 Reorder the terms: 62 + 9x + -1x2 = 5 + -5 + x2 + -1x2 Combine like terms: 5 + -5 = 0 62 + 9x + -1x2 = 0 + x2 + -1x2 62 + 9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 62 + 9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -62 + -9x + x2 = 0 Move the constant term to the right: Add '62' to each side of the equation. -62 + -9x + 62 + x2 = 0 + 62 Reorder the terms: -62 + 62 + -9x + x2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + -9x + x2 = 0 + 62 -9x + x2 = 0 + 62 Combine like terms: 0 + 62 = 62 -9x + x2 = 62 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 = 62 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 62 + 20.25 Combine like terms: 62 + 20.25 = 82.25 20.25 + -9x + x2 = 82.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 82.25 Calculate the square root of the right side: 9.069178574 Break this problem into two subproblems by setting (x + -4.5) equal to 9.069178574 and -9.069178574.Subproblem 1
x + -4.5 = 9.069178574 Simplifying x + -4.5 = 9.069178574 Reorder the terms: -4.5 + x = 9.069178574 Solving -4.5 + x = 9.069178574 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 = 9.069178574 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 9.069178574 + 4.5 x = 9.069178574 + 4.5 Combine like terms: 9.069178574 + 4.5 = 13.569178574 x = 13.569178574 Simplifying x = 13.569178574Subproblem 2
x + -4.5 = -9.069178574 Simplifying x + -4.5 = -9.069178574 Reorder the terms: -4.5 + x = -9.069178574 Solving -4.5 + x = -9.069178574 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 = -9.069178574 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -9.069178574 + 4.5 x = -9.069178574 + 4.5 Combine like terms: -9.069178574 + 4.5 = -4.569178574 x = -4.569178574 Simplifying x = -4.569178574Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.569178574, -4.569178574}
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