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Simplifying 9x + 4 = 5.5x + 0.5x2 Reorder the terms: 4 + 9x = 5.5x + 0.5x2 Solving 4 + 9x = 5.5x + 0.5x2 Solving for variable 'x'. Combine like terms: 9x + -5.5x = 3.5x 4 + 3.5x + -0.5x2 = 5.5x + 0.5x2 + -5.5x + -0.5x2 Reorder the terms: 4 + 3.5x + -0.5x2 = 5.5x + -5.5x + 0.5x2 + -0.5x2 Combine like terms: 5.5x + -5.5x = 0.0 4 + 3.5x + -0.5x2 = 0.0 + 0.5x2 + -0.5x2 4 + 3.5x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 4 + 3.5x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -8 + -7x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -7x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -7x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -7x + x2 = 0 + 8 -7x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -7x + x2 = 8 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 8 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 8 + 12.25 Combine like terms: 8 + 12.25 = 20.25 12.25 + -7x + x2 = 20.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 20.25 Calculate the square root of the right side: 4.5 Break this problem into two subproblems by setting (x + -3.5) equal to 4.5 and -4.5.Subproblem 1
x + -3.5 = 4.5 Simplifying x + -3.5 = 4.5 Reorder the terms: -3.5 + x = 4.5 Solving -3.5 + x = 4.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 4.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.5 + 3.5 x = 4.5 + 3.5 Combine like terms: 4.5 + 3.5 = 8 x = 8 Simplifying x = 8Subproblem 2
x + -3.5 = -4.5 Simplifying x + -3.5 = -4.5 Reorder the terms: -3.5 + x = -4.5 Solving -3.5 + x = -4.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -4.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.5 + 3.5 x = -4.5 + 3.5 Combine like terms: -4.5 + 3.5 = -1 x = -1 Simplifying x = -1Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, -1}
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