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Simplifying -3.6x2 + 7.2x + 13.824 = 0 Reorder the terms: 13.824 + 7.2x + -3.6x2 = 0 Solving 13.824 + 7.2x + -3.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3.6 the coefficient of the squared term: Divide each side by '-3.6'. -3.84 + -2x + x2 = 0 Move the constant term to the right: Add '3.84' to each side of the equation. -3.84 + -2x + 3.84 + x2 = 0 + 3.84 Reorder the terms: -3.84 + 3.84 + -2x + x2 = 0 + 3.84 Combine like terms: -3.84 + 3.84 = 0.00 0.00 + -2x + x2 = 0 + 3.84 -2x + x2 = 0 + 3.84 Combine like terms: 0 + 3.84 = 3.84 -2x + x2 = 3.84 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 = 3.84 + 1 Reorder the terms: 1 + -2x + x2 = 3.84 + 1 Combine like terms: 3.84 + 1 = 4.84 1 + -2x + x2 = 4.84 Factor a perfect square on the left side: (x + -1)(x + -1) = 4.84 Calculate the square root of the right side: 2.2 Break this problem into two subproblems by setting (x + -1) equal to 2.2 and -2.2.Subproblem 1
x + -1 = 2.2 Simplifying x + -1 = 2.2 Reorder the terms: -1 + x = 2.2 Solving -1 + x = 2.2 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 = 2.2 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.2 + 1 x = 2.2 + 1 Combine like terms: 2.2 + 1 = 3.2 x = 3.2 Simplifying x = 3.2Subproblem 2
x + -1 = -2.2 Simplifying x + -1 = -2.2 Reorder the terms: -1 + x = -2.2 Solving -1 + x = -2.2 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 = -2.2 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.2 + 1 x = -2.2 + 1 Combine like terms: -2.2 + 1 = -1.2 x = -1.2 Simplifying x = -1.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2, -1.2}
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