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Simplifying -0.5x2 + 3.5x + 9 = 0 Reorder the terms: 9 + 3.5x + -0.5x2 = 0 Solving 9 + 3.5x + -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'. -18 + -7x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -7x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -7x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -7x + x2 = 0 + 18 -7x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -7x + x2 = 18 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 18 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 18 + 12.25 Combine like terms: 18 + 12.25 = 30.25 12.25 + -7x + x2 = 30.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 30.25 Calculate the square root of the right side: 5.5 Break this problem into two subproblems by setting (x + -3.5) equal to 5.5 and -5.5.Subproblem 1
x + -3.5 = 5.5 Simplifying x + -3.5 = 5.5 Reorder the terms: -3.5 + x = 5.5 Solving -3.5 + x = 5.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 5.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 5.5 + 3.5 x = 5.5 + 3.5 Combine like terms: 5.5 + 3.5 = 9 x = 9 Simplifying x = 9Subproblem 2
x + -3.5 = -5.5 Simplifying x + -3.5 = -5.5 Reorder the terms: -3.5 + x = -5.5 Solving -3.5 + x = -5.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -5.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -5.5 + 3.5 x = -5.5 + 3.5 Combine like terms: -5.5 + 3.5 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {9, -2}
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