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Simplifying 0.3x2 + -3.3x + 8.4 = 0 Reorder the terms: 8.4 + -3.3x + 0.3x2 = 0 Solving 8.4 + -3.3x + 0.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. 28 + -11x + x2 = 0 Move the constant term to the right: Add '-28' to each side of the equation. 28 + -11x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + -11x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -11x + x2 = 0 + -28 -11x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 -11x + x2 = -28 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -28 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -28 + 30.25 Combine like terms: -28 + 30.25 = 2.25 30.25 + -11x + x2 = 2.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 2.25 Calculate the square root of the right side: 1.5 Break this problem into two subproblems by setting (x + -5.5) equal to 1.5 and -1.5.Subproblem 1
x + -5.5 = 1.5 Simplifying x + -5.5 = 1.5 Reorder the terms: -5.5 + x = 1.5 Solving -5.5 + x = 1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 1.5 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 1.5 + 5.5 x = 1.5 + 5.5 Combine like terms: 1.5 + 5.5 = 7 x = 7 Simplifying x = 7Subproblem 2
x + -5.5 = -1.5 Simplifying x + -5.5 = -1.5 Reorder the terms: -5.5 + x = -1.5 Solving -5.5 + x = -1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -1.5 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -1.5 + 5.5 x = -1.5 + 5.5 Combine like terms: -1.5 + 5.5 = 4 x = 4 Simplifying x = 4Solution
The solution to the problem is based on the solutions from the subproblems. x = {7, 4}
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