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Simplifying -1.6x2 + -3.2x + 18 = 0 Reorder the terms: 18 + -3.2x + -1.6x2 = 0 Solving 18 + -3.2x + -1.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1.6 the coefficient of the squared term: Divide each side by '-1.6'. -11.25 + 2x + x2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + 2x + 11.25 + x2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + 2x + x2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + 2x + x2 = 0 + 11.25 2x + x2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 2x + x2 = 11.25 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 11.25 + 1 Reorder the terms: 1 + 2x + x2 = 11.25 + 1 Combine like terms: 11.25 + 1 = 12.25 1 + 2x + x2 = 12.25 Factor a perfect square on the left side: (x + 1)(x + 1) = 12.25 Calculate the square root of the right side: 3.5 Break this problem into two subproblems by setting (x + 1) equal to 3.5 and -3.5.Subproblem 1
x + 1 = 3.5 Simplifying x + 1 = 3.5 Reorder the terms: 1 + x = 3.5 Solving 1 + x = 3.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.5 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.5 + -1 x = 3.5 + -1 Combine like terms: 3.5 + -1 = 2.5 x = 2.5 Simplifying x = 2.5Subproblem 2
x + 1 = -3.5 Simplifying x + 1 = -3.5 Reorder the terms: 1 + x = -3.5 Solving 1 + x = -3.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.5 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.5 + -1 x = -3.5 + -1 Combine like terms: -3.5 + -1 = -4.5 x = -4.5 Simplifying x = -4.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5, -4.5}
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