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Simplifying 2x2 + -6x + 5 = 8.5 Reorder the terms: 5 + -6x + 2x2 = 8.5 Solving 5 + -6x + 2x2 = 8.5 Solving for variable 'x'. Reorder the terms: 5 + -8.5 + -6x + 2x2 = 8.5 + -8.5 Combine like terms: 5 + -8.5 = -3.5 -3.5 + -6x + 2x2 = 8.5 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 -3.5 + -6x + 2x2 = 0.0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.75 + -3x + x2 = 0.0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -3x + 1.75 + x2 = 0.0 + 1.75 Reorder the terms: -1.75 + 1.75 + -3x + x2 = 0.0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -3x + x2 = 0.0 + 1.75 -3x + x2 = 0.0 + 1.75 Combine like terms: 0.0 + 1.75 = 1.75 -3x + x2 = 1.75 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 = 1.75 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 1.75 + 2.25 Combine like terms: 1.75 + 2.25 = 4 2.25 + -3x + x2 = 4 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (x + -1.5) equal to 2 and -2.Subproblem 1
x + -1.5 = 2 Simplifying x + -1.5 = 2 Reorder the terms: -1.5 + x = 2 Solving -1.5 + x = 2 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 = 2 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2 + 1.5 x = 2 + 1.5 Combine like terms: 2 + 1.5 = 3.5 x = 3.5 Simplifying x = 3.5Subproblem 2
x + -1.5 = -2 Simplifying x + -1.5 = -2 Reorder the terms: -1.5 + x = -2 Solving -1.5 + x = -2 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 = -2 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2 + 1.5 x = -2 + 1.5 Combine like terms: -2 + 1.5 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.5, -0.5}
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