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Simplifying -2x * x + 8x + 16.5 = 0 Multiply x * x -2x2 + 8x + 16.5 = 0 Reorder the terms: 16.5 + 8x + -2x2 = 0 Solving 16.5 + 8x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -8.25 + -4x + x2 = 0 Move the constant term to the right: Add '8.25' to each side of the equation. -8.25 + -4x + 8.25 + x2 = 0 + 8.25 Reorder the terms: -8.25 + 8.25 + -4x + x2 = 0 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + -4x + x2 = 0 + 8.25 -4x + x2 = 0 + 8.25 Combine like terms: 0 + 8.25 = 8.25 -4x + x2 = 8.25 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 = 8.25 + 4 Reorder the terms: 4 + -4x + x2 = 8.25 + 4 Combine like terms: 8.25 + 4 = 12.25 4 + -4x + x2 = 12.25 Factor a perfect square on the left side: (x + -2)(x + -2) = 12.25 Calculate the square root of the right side: 3.5 Break this problem into two subproblems by setting (x + -2) equal to 3.5 and -3.5.Subproblem 1
x + -2 = 3.5 Simplifying x + -2 = 3.5 Reorder the terms: -2 + x = 3.5 Solving -2 + x = 3.5 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 = 3.5 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.5 + 2 x = 3.5 + 2 Combine like terms: 3.5 + 2 = 5.5 x = 5.5 Simplifying x = 5.5Subproblem 2
x + -2 = -3.5 Simplifying x + -2 = -3.5 Reorder the terms: -2 + x = -3.5 Solving -2 + x = -3.5 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 = -3.5 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.5 + 2 x = -3.5 + 2 Combine like terms: -3.5 + 2 = -1.5 x = -1.5 Simplifying x = -1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.5, -1.5}
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