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Simplifying 0.5x2 + -4.5x + 4 = 0 Reorder the terms: 4 + -4.5x + 0.5x2 = 0 Solving 4 + -4.5x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 8 + -9x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -9x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -9x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -9x + x2 = 0 + -8 -9x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -9x + x2 = -8 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 = -8 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -8 + 20.25 Combine like terms: -8 + 20.25 = 12.25 20.25 + -9x + x2 = 12.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 12.25 Calculate the square root of the right side: 3.5 Break this problem into two subproblems by setting (x + -4.5) equal to 3.5 and -3.5.Subproblem 1
x + -4.5 = 3.5 Simplifying x + -4.5 = 3.5 Reorder the terms: -4.5 + x = 3.5 Solving -4.5 + x = 3.5 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 = 3.5 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 3.5 + 4.5 x = 3.5 + 4.5 Combine like terms: 3.5 + 4.5 = 8 x = 8 Simplifying x = 8Subproblem 2
x + -4.5 = -3.5 Simplifying x + -4.5 = -3.5 Reorder the terms: -4.5 + x = -3.5 Solving -4.5 + x = -3.5 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 = -3.5 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -3.5 + 4.5 x = -3.5 + 4.5 Combine like terms: -3.5 + 4.5 = 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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