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Simplifying 2x2 + -6x = 13.5 Reorder the terms: -6x + 2x2 = 13.5 Solving -6x + 2x2 = 13.5 Solving for variable 'x'. Reorder the terms: -13.5 + -6x + 2x2 = 13.5 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 -13.5 + -6x + 2x2 = 0.0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6.75 + -3x + x2 = 0.0 Move the constant term to the right: Add '6.75' to each side of the equation. -6.75 + -3x + 6.75 + x2 = 0.0 + 6.75 Reorder the terms: -6.75 + 6.75 + -3x + x2 = 0.0 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + -3x + x2 = 0.0 + 6.75 -3x + x2 = 0.0 + 6.75 Combine like terms: 0.0 + 6.75 = 6.75 -3x + x2 = 6.75 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 6.75 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 6.75 + 2.25 Combine like terms: 6.75 + 2.25 = 9 2.25 + -3x + x2 = 9 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 9 Calculate the square root of the right side: 3 Break this problem into two subproblems by setting (x + -1.5) equal to 3 and -3.Subproblem 1
x + -1.5 = 3 Simplifying x + -1.5 = 3 Reorder the terms: -1.5 + x = 3 Solving -1.5 + x = 3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3 + 1.5 x = 3 + 1.5 Combine like terms: 3 + 1.5 = 4.5 x = 4.5 Simplifying x = 4.5Subproblem 2
x + -1.5 = -3 Simplifying x + -1.5 = -3 Reorder the terms: -1.5 + x = -3 Solving -1.5 + x = -3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3 + 1.5 x = -3 + 1.5 Combine like terms: -3 + 1.5 = -1.5 x = -1.5 Simplifying x = -1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.5, -1.5}
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