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Simplifying -0.33x2 + -5.94x = 26.4 Reorder the terms: -5.94x + -0.33x2 = 26.4 Solving -5.94x + -0.33x2 = 26.4 Solving for variable 'x'. Reorder the terms: -26.4 + -5.94x + -0.33x2 = 26.4 + -26.4 Combine like terms: 26.4 + -26.4 = 0.0 -26.4 + -5.94x + -0.33x2 = 0.0 Begin completing the square. Divide all terms by -0.33 the coefficient of the squared term: Divide each side by '-0.33'. 80 + 18x + x2 = 0 Move the constant term to the right: Add '-80' to each side of the equation. 80 + 18x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + 18x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + 18x + x2 = 0 + -80 18x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 18x + x2 = -80 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = -80 + 81 Reorder the terms: 81 + 18x + x2 = -80 + 81 Combine like terms: -80 + 81 = 1 81 + 18x + x2 = 1 Factor a perfect square on the left side: (x + 9)(x + 9) = 1 Calculate the square root of the right side: 1 Break this problem into two subproblems by setting (x + 9) equal to 1 and -1.Subproblem 1
x + 9 = 1 Simplifying x + 9 = 1 Reorder the terms: 9 + x = 1 Solving 9 + x = 1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 1 + -9 Combine like terms: 9 + -9 = 0 0 + x = 1 + -9 x = 1 + -9 Combine like terms: 1 + -9 = -8 x = -8 Simplifying x = -8Subproblem 2
x + 9 = -1 Simplifying x + 9 = -1 Reorder the terms: 9 + x = -1 Solving 9 + x = -1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -1 + -9 Combine like terms: 9 + -9 = 0 0 + x = -1 + -9 x = -1 + -9 Combine like terms: -1 + -9 = -10 x = -10 Simplifying x = -10Solution
The solution to the problem is based on the solutions from the subproblems. x = {-8, -10}
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