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Simplifying 0 = -0.6x2 + 7.2x + -6.6 Reorder the terms: 0 = -6.6 + 7.2x + -0.6x2 Solving 0 = -6.6 + 7.2x + -0.6x2 Solving for variable 'x'. Combine like terms: 0 + 6.6 = 6.6 6.6 + -7.2x + 0.6x2 = -6.6 + 7.2x + -0.6x2 + 6.6 + -7.2x + 0.6x2 Reorder the terms: 6.6 + -7.2x + 0.6x2 = -6.6 + 6.6 + 7.2x + -7.2x + -0.6x2 + 0.6x2 Combine like terms: -6.6 + 6.6 = 0.0 6.6 + -7.2x + 0.6x2 = 0.0 + 7.2x + -7.2x + -0.6x2 + 0.6x2 6.6 + -7.2x + 0.6x2 = 7.2x + -7.2x + -0.6x2 + 0.6x2 Combine like terms: 7.2x + -7.2x = 0.0 6.6 + -7.2x + 0.6x2 = 0.0 + -0.6x2 + 0.6x2 6.6 + -7.2x + 0.6x2 = -0.6x2 + 0.6x2 Combine like terms: -0.6x2 + 0.6x2 = 0.0 6.6 + -7.2x + 0.6x2 = 0.0 Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. 11 + -12x + x2 = 0 Move the constant term to the right: Add '-11' to each side of the equation. 11 + -12x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -12x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -12x + x2 = 0 + -11 -12x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -12x + x2 = -11 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -11 + 36 Reorder the terms: 36 + -12x + x2 = -11 + 36 Combine like terms: -11 + 36 = 25 36 + -12x + x2 = 25 Factor a perfect square on the left side: (x + -6)(x + -6) = 25 Calculate the square root of the right side: 5 Break this problem into two subproblems by setting (x + -6) equal to 5 and -5.Subproblem 1
x + -6 = 5 Simplifying x + -6 = 5 Reorder the terms: -6 + x = 5 Solving -6 + x = 5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 5 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5 + 6 x = 5 + 6 Combine like terms: 5 + 6 = 11 x = 11 Simplifying x = 11Subproblem 2
x + -6 = -5 Simplifying x + -6 = -5 Reorder the terms: -6 + x = -5 Solving -6 + x = -5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -5 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5 + 6 x = -5 + 6 Combine like terms: -5 + 6 = 1 x = 1 Simplifying x = 1Solution
The solution to the problem is based on the solutions from the subproblems. x = {11, 1}
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