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Simplifying 0.3x2 + 54x + -12 = 80 Reorder the terms: -12 + 54x + 0.3x2 = 80 Solving -12 + 54x + 0.3x2 = 80 Solving for variable 'x'. Reorder the terms: -12 + -80 + 54x + 0.3x2 = 80 + -80 Combine like terms: -12 + -80 = -92 -92 + 54x + 0.3x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -92 + 54x + 0.3x2 = 0 Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. -306.6666667 + 180x + x2 = 0 Move the constant term to the right: Add '306.6666667' to each side of the equation. -306.6666667 + 180x + 306.6666667 + x2 = 0 + 306.6666667 Reorder the terms: -306.6666667 + 306.6666667 + 180x + x2 = 0 + 306.6666667 Combine like terms: -306.6666667 + 306.6666667 = 0.0000000 0.0000000 + 180x + x2 = 0 + 306.6666667 180x + x2 = 0 + 306.6666667 Combine like terms: 0 + 306.6666667 = 306.6666667 180x + x2 = 306.6666667 The x term is 180x. Take half its coefficient (90). Square it (8100) and add it to both sides. Add '8100' to each side of the equation. 180x + 8100 + x2 = 306.6666667 + 8100 Reorder the terms: 8100 + 180x + x2 = 306.6666667 + 8100 Combine like terms: 306.6666667 + 8100 = 8406.6666667 8100 + 180x + x2 = 8406.6666667 Factor a perfect square on the left side: (x + 90)(x + 90) = 8406.6666667 Calculate the square root of the right side: 91.687876334 Break this problem into two subproblems by setting (x + 90) equal to 91.687876334 and -91.687876334.Subproblem 1
x + 90 = 91.687876334 Simplifying x + 90 = 91.687876334 Reorder the terms: 90 + x = 91.687876334 Solving 90 + x = 91.687876334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-90' to each side of the equation. 90 + -90 + x = 91.687876334 + -90 Combine like terms: 90 + -90 = 0 0 + x = 91.687876334 + -90 x = 91.687876334 + -90 Combine like terms: 91.687876334 + -90 = 1.687876334 x = 1.687876334 Simplifying x = 1.687876334Subproblem 2
x + 90 = -91.687876334 Simplifying x + 90 = -91.687876334 Reorder the terms: 90 + x = -91.687876334 Solving 90 + x = -91.687876334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-90' to each side of the equation. 90 + -90 + x = -91.687876334 + -90 Combine like terms: 90 + -90 = 0 0 + x = -91.687876334 + -90 x = -91.687876334 + -90 Combine like terms: -91.687876334 + -90 = -181.687876334 x = -181.687876334 Simplifying x = -181.687876334Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.687876334, -181.687876334}
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