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Simplifying 5x2 + -48x + 104 = 0 Reorder the terms: 104 + -48x + 5x2 = 0 Solving 104 + -48x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 20.8 + -9.6x + x2 = 0 Move the constant term to the right: Add '-20.8' to each side of the equation. 20.8 + -9.6x + -20.8 + x2 = 0 + -20.8 Reorder the terms: 20.8 + -20.8 + -9.6x + x2 = 0 + -20.8 Combine like terms: 20.8 + -20.8 = 0.0 0.0 + -9.6x + x2 = 0 + -20.8 -9.6x + x2 = 0 + -20.8 Combine like terms: 0 + -20.8 = -20.8 -9.6x + x2 = -20.8 The x term is -9.6x. Take half its coefficient (-4.8). Square it (23.04) and add it to both sides. Add '23.04' to each side of the equation. -9.6x + 23.04 + x2 = -20.8 + 23.04 Reorder the terms: 23.04 + -9.6x + x2 = -20.8 + 23.04 Combine like terms: -20.8 + 23.04 = 2.24 23.04 + -9.6x + x2 = 2.24 Factor a perfect square on the left side: (x + -4.8)(x + -4.8) = 2.24 Calculate the square root of the right side: 1.496662955 Break this problem into two subproblems by setting (x + -4.8) equal to 1.496662955 and -1.496662955.Subproblem 1
x + -4.8 = 1.496662955 Simplifying x + -4.8 = 1.496662955 Reorder the terms: -4.8 + x = 1.496662955 Solving -4.8 + x = 1.496662955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + x = 1.496662955 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = 1.496662955 + 4.8 x = 1.496662955 + 4.8 Combine like terms: 1.496662955 + 4.8 = 6.296662955 x = 6.296662955 Simplifying x = 6.296662955Subproblem 2
x + -4.8 = -1.496662955 Simplifying x + -4.8 = -1.496662955 Reorder the terms: -4.8 + x = -1.496662955 Solving -4.8 + x = -1.496662955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + x = -1.496662955 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = -1.496662955 + 4.8 x = -1.496662955 + 4.8 Combine like terms: -1.496662955 + 4.8 = 3.303337045 x = 3.303337045 Simplifying x = 3.303337045Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.296662955, 3.303337045}
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