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Simplifying 3x2 + -30x + 135 = 80 Reorder the terms: 135 + -30x + 3x2 = 80 Solving 135 + -30x + 3x2 = 80 Solving for variable 'x'. Reorder the terms: 135 + -80 + -30x + 3x2 = 80 + -80 Combine like terms: 135 + -80 = 55 55 + -30x + 3x2 = 80 + -80 Combine like terms: 80 + -80 = 0 55 + -30x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 18.33333333 + -10x + x2 = 0 Move the constant term to the right: Add '-18.33333333' to each side of the equation. 18.33333333 + -10x + -18.33333333 + x2 = 0 + -18.33333333 Reorder the terms: 18.33333333 + -18.33333333 + -10x + x2 = 0 + -18.33333333 Combine like terms: 18.33333333 + -18.33333333 = 0.00000000 0.00000000 + -10x + x2 = 0 + -18.33333333 -10x + x2 = 0 + -18.33333333 Combine like terms: 0 + -18.33333333 = -18.33333333 -10x + x2 = -18.33333333 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -18.33333333 + 25 Reorder the terms: 25 + -10x + x2 = -18.33333333 + 25 Combine like terms: -18.33333333 + 25 = 6.66666667 25 + -10x + x2 = 6.66666667 Factor a perfect square on the left side: (x + -5)(x + -5) = 6.66666667 Calculate the square root of the right side: 2.581988898 Break this problem into two subproblems by setting (x + -5) equal to 2.581988898 and -2.581988898.Subproblem 1
x + -5 = 2.581988898 Simplifying x + -5 = 2.581988898 Reorder the terms: -5 + x = 2.581988898 Solving -5 + x = 2.581988898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 2.581988898 + 5 Combine like terms: -5 + 5 = 0 0 + x = 2.581988898 + 5 x = 2.581988898 + 5 Combine like terms: 2.581988898 + 5 = 7.581988898 x = 7.581988898 Simplifying x = 7.581988898Subproblem 2
x + -5 = -2.581988898 Simplifying x + -5 = -2.581988898 Reorder the terms: -5 + x = -2.581988898 Solving -5 + x = -2.581988898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -2.581988898 + 5 Combine like terms: -5 + 5 = 0 0 + x = -2.581988898 + 5 x = -2.581988898 + 5 Combine like terms: -2.581988898 + 5 = 2.418011102 x = 2.418011102 Simplifying x = 2.418011102Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.581988898, 2.418011102}
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