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Simplifying 0 = -0.06x2 + 9.6x + 5.4 Reorder the terms: 0 = 5.4 + 9.6x + -0.06x2 Solving 0 = 5.4 + 9.6x + -0.06x2 Solving for variable 'x'. Combine like terms: 0 + -5.4 = -5.4 -5.4 + -9.6x + 0.06x2 = 5.4 + 9.6x + -0.06x2 + -5.4 + -9.6x + 0.06x2 Reorder the terms: -5.4 + -9.6x + 0.06x2 = 5.4 + -5.4 + 9.6x + -9.6x + -0.06x2 + 0.06x2 Combine like terms: 5.4 + -5.4 = 0.0 -5.4 + -9.6x + 0.06x2 = 0.0 + 9.6x + -9.6x + -0.06x2 + 0.06x2 -5.4 + -9.6x + 0.06x2 = 9.6x + -9.6x + -0.06x2 + 0.06x2 Combine like terms: 9.6x + -9.6x = 0.0 -5.4 + -9.6x + 0.06x2 = 0.0 + -0.06x2 + 0.06x2 -5.4 + -9.6x + 0.06x2 = -0.06x2 + 0.06x2 Combine like terms: -0.06x2 + 0.06x2 = 0.00 -5.4 + -9.6x + 0.06x2 = 0.00 Begin completing the square. Divide all terms by 0.06 the coefficient of the squared term: Divide each side by '0.06'. -90 + -160x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + -160x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + -160x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -160x + x2 = 0 + 90 -160x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 -160x + x2 = 90 The x term is -160x. Take half its coefficient (-80). Square it (6400) and add it to both sides. Add '6400' to each side of the equation. -160x + 6400 + x2 = 90 + 6400 Reorder the terms: 6400 + -160x + x2 = 90 + 6400 Combine like terms: 90 + 6400 = 6490 6400 + -160x + x2 = 6490 Factor a perfect square on the left side: (x + -80)(x + -80) = 6490 Calculate the square root of the right side: 80.560536244 Break this problem into two subproblems by setting (x + -80) equal to 80.560536244 and -80.560536244.Subproblem 1
x + -80 = 80.560536244 Simplifying x + -80 = 80.560536244 Reorder the terms: -80 + x = 80.560536244 Solving -80 + x = 80.560536244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = 80.560536244 + 80 Combine like terms: -80 + 80 = 0 0 + x = 80.560536244 + 80 x = 80.560536244 + 80 Combine like terms: 80.560536244 + 80 = 160.560536244 x = 160.560536244 Simplifying x = 160.560536244Subproblem 2
x + -80 = -80.560536244 Simplifying x + -80 = -80.560536244 Reorder the terms: -80 + x = -80.560536244 Solving -80 + x = -80.560536244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = -80.560536244 + 80 Combine like terms: -80 + 80 = 0 0 + x = -80.560536244 + 80 x = -80.560536244 + 80 Combine like terms: -80.560536244 + 80 = -0.560536244 x = -0.560536244 Simplifying x = -0.560536244Solution
The solution to the problem is based on the solutions from the subproblems. x = {160.560536244, -0.560536244}
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