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Simplifying 0.5x2 + -3x + 4.5 = 0 Reorder the terms: 4.5 + -3x + 0.5x2 = 0 Solving 4.5 + -3x + 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'. 9 + -6x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -6x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -6x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -6x + x2 = 0 + -9 -6x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -6x + x2 = -9 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -9 + 9 Reorder the terms: 9 + -6x + x2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + -6x + x2 = 0 Factor a perfect square on the left side: (x + -3)(x + -3) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (x + -3) equal to 0 and 0.Subproblem 1
x + -3 = 0 Simplifying x + -3 = 0 Reorder the terms: -3 + x = 0 Solving -3 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Subproblem 2
x + -3 = 0 Simplifying x + -3 = 0 Reorder the terms: -3 + x = 0 Solving -3 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Solution
The solution to the problem is based on the solutions from the subproblems. x = {3, 3}
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