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Simplifying 2.5x2 + -16.5x + 6 = 0 Reorder the terms: 6 + -16.5x + 2.5x2 = 0 Solving 6 + -16.5x + 2.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. 2.4 + -6.6x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -6.6x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -6.6x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -6.6x + x2 = 0 + -2.4 -6.6x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -6.6x + x2 = -2.4 The x term is -6.6x. Take half its coefficient (-3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. -6.6x + 10.89 + x2 = -2.4 + 10.89 Reorder the terms: 10.89 + -6.6x + x2 = -2.4 + 10.89 Combine like terms: -2.4 + 10.89 = 8.49 10.89 + -6.6x + x2 = 8.49 Factor a perfect square on the left side: (x + -3.3)(x + -3.3) = 8.49 Calculate the square root of the right side: 2.913760457 Break this problem into two subproblems by setting (x + -3.3) equal to 2.913760457 and -2.913760457.Subproblem 1
x + -3.3 = 2.913760457 Simplifying x + -3.3 = 2.913760457 Reorder the terms: -3.3 + x = 2.913760457 Solving -3.3 + x = 2.913760457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + x = 2.913760457 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x = 2.913760457 + 3.3 x = 2.913760457 + 3.3 Combine like terms: 2.913760457 + 3.3 = 6.213760457 x = 6.213760457 Simplifying x = 6.213760457Subproblem 2
x + -3.3 = -2.913760457 Simplifying x + -3.3 = -2.913760457 Reorder the terms: -3.3 + x = -2.913760457 Solving -3.3 + x = -2.913760457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + x = -2.913760457 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x = -2.913760457 + 3.3 x = -2.913760457 + 3.3 Combine like terms: -2.913760457 + 3.3 = 0.386239543 x = 0.386239543 Simplifying x = 0.386239543Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.213760457, 0.386239543}
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