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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 = 7793.3333333 8100 + -180x + x2 = 7793.3333333 Factor a perfect square on the left side: (x + -90)(x + -90) = 7793.3333333 Calculate the square root of the right side: 88.279858027 Break this problem into two subproblems by setting (x + -90) equal to 88.279858027 and -88.279858027.Subproblem 1
x + -90 = 88.279858027 Simplifying x + -90 = 88.279858027 Reorder the terms: -90 + x = 88.279858027 Solving -90 + x = 88.279858027 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 = 88.279858027 + 90 Combine like terms: -90 + 90 = 0 0 + x = 88.279858027 + 90 x = 88.279858027 + 90 Combine like terms: 88.279858027 + 90 = 178.279858027 x = 178.279858027 Simplifying x = 178.279858027Subproblem 2
x + -90 = -88.279858027 Simplifying x + -90 = -88.279858027 Reorder the terms: -90 + x = -88.279858027 Solving -90 + x = -88.279858027 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 = -88.279858027 + 90 Combine like terms: -90 + 90 = 0 0 + x = -88.279858027 + 90 x = -88.279858027 + 90 Combine like terms: -88.279858027 + 90 = 1.720141973 x = 1.720141973 Simplifying x = 1.720141973Solution
The solution to the problem is based on the solutions from the subproblems. x = {178.279858027, 1.720141973}
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