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Simplifying 5x2 + -44x + 12 = 6 Reorder the terms: 12 + -44x + 5x2 = 6 Solving 12 + -44x + 5x2 = 6 Solving for variable 'x'. Reorder the terms: 12 + -6 + -44x + 5x2 = 6 + -6 Combine like terms: 12 + -6 = 6 6 + -44x + 5x2 = 6 + -6 Combine like terms: 6 + -6 = 0 6 + -44x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.2 + -8.8x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + -8.8x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + -8.8x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + -8.8x + x2 = 0 + -1.2 -8.8x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 -8.8x + x2 = -1.2 The x term is -8.8x. Take half its coefficient (-4.4). Square it (19.36) and add it to both sides. Add '19.36' to each side of the equation. -8.8x + 19.36 + x2 = -1.2 + 19.36 Reorder the terms: 19.36 + -8.8x + x2 = -1.2 + 19.36 Combine like terms: -1.2 + 19.36 = 18.16 19.36 + -8.8x + x2 = 18.16 Factor a perfect square on the left side: (x + -4.4)(x + -4.4) = 18.16 Calculate the square root of the right side: 4.261455151 Break this problem into two subproblems by setting (x + -4.4) equal to 4.261455151 and -4.261455151.Subproblem 1
x + -4.4 = 4.261455151 Simplifying x + -4.4 = 4.261455151 Reorder the terms: -4.4 + x = 4.261455151 Solving -4.4 + x = 4.261455151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.4' to each side of the equation. -4.4 + 4.4 + x = 4.261455151 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + x = 4.261455151 + 4.4 x = 4.261455151 + 4.4 Combine like terms: 4.261455151 + 4.4 = 8.661455151 x = 8.661455151 Simplifying x = 8.661455151Subproblem 2
x + -4.4 = -4.261455151 Simplifying x + -4.4 = -4.261455151 Reorder the terms: -4.4 + x = -4.261455151 Solving -4.4 + x = -4.261455151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.4' to each side of the equation. -4.4 + 4.4 + x = -4.261455151 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + x = -4.261455151 + 4.4 x = -4.261455151 + 4.4 Combine like terms: -4.261455151 + 4.4 = 0.138544849 x = 0.138544849 Simplifying x = 0.138544849Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.661455151, 0.138544849}
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