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Simplifying 1.5x2 + -6x + 4.5 = 0 Reorder the terms: 4.5 + -6x + 1.5x2 = 0 Solving 4.5 + -6x + 1.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. 3 + -4x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -4x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -4x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x + x2 = 0 + -3 -4x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -4x + x2 = -3 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -3 + 4 Reorder the terms: 4 + -4x + x2 = -3 + 4 Combine like terms: -3 + 4 = 1 4 + -4x + x2 = 1 Factor a perfect square on the left side: (x + -2)(x + -2) = 1 Calculate the square root of the right side: 1 Break this problem into two subproblems by setting (x + -2) equal to 1 and -1.Subproblem 1
x + -2 = 1 Simplifying x + -2 = 1 Reorder the terms: -2 + x = 1 Solving -2 + x = 1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1 + 2 x = 1 + 2 Combine like terms: 1 + 2 = 3 x = 3 Simplifying x = 3Subproblem 2
x + -2 = -1 Simplifying x + -2 = -1 Reorder the terms: -2 + x = -1 Solving -2 + x = -1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1 + 2 x = -1 + 2 Combine like terms: -1 + 2 = 1 x = 1 Simplifying x = 1Solution
The solution to the problem is based on the solutions from the subproblems. x = {3, 1}
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