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Simplifying 0 = -1.5x2 + 75x + 20 Reorder the terms: 0 = 20 + 75x + -1.5x2 Solving 0 = 20 + 75x + -1.5x2 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + -75x + 1.5x2 = 20 + 75x + -1.5x2 + -20 + -75x + 1.5x2 Reorder the terms: -20 + -75x + 1.5x2 = 20 + -20 + 75x + -75x + -1.5x2 + 1.5x2 Combine like terms: 20 + -20 = 0 -20 + -75x + 1.5x2 = 0 + 75x + -75x + -1.5x2 + 1.5x2 -20 + -75x + 1.5x2 = 75x + -75x + -1.5x2 + 1.5x2 Combine like terms: 75x + -75x = 0 -20 + -75x + 1.5x2 = 0 + -1.5x2 + 1.5x2 -20 + -75x + 1.5x2 = -1.5x2 + 1.5x2 Combine like terms: -1.5x2 + 1.5x2 = 0.0 -20 + -75x + 1.5x2 = 0.0 Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. -13.33333333 + -50x + x2 = 0 Move the constant term to the right: Add '13.33333333' to each side of the equation. -13.33333333 + -50x + 13.33333333 + x2 = 0 + 13.33333333 Reorder the terms: -13.33333333 + 13.33333333 + -50x + x2 = 0 + 13.33333333 Combine like terms: -13.33333333 + 13.33333333 = 0.00000000 0.00000000 + -50x + x2 = 0 + 13.33333333 -50x + x2 = 0 + 13.33333333 Combine like terms: 0 + 13.33333333 = 13.33333333 -50x + x2 = 13.33333333 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = 13.33333333 + 625 Reorder the terms: 625 + -50x + x2 = 13.33333333 + 625 Combine like terms: 13.33333333 + 625 = 638.33333333 625 + -50x + x2 = 638.33333333 Factor a perfect square on the left side: (x + -25)(x + -25) = 638.33333333 Calculate the square root of the right side: 25.265259415 Break this problem into two subproblems by setting (x + -25) equal to 25.265259415 and -25.265259415.Subproblem 1
x + -25 = 25.265259415 Simplifying x + -25 = 25.265259415 Reorder the terms: -25 + x = 25.265259415 Solving -25 + x = 25.265259415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 25.265259415 + 25 Combine like terms: -25 + 25 = 0 0 + x = 25.265259415 + 25 x = 25.265259415 + 25 Combine like terms: 25.265259415 + 25 = 50.265259415 x = 50.265259415 Simplifying x = 50.265259415Subproblem 2
x + -25 = -25.265259415 Simplifying x + -25 = -25.265259415 Reorder the terms: -25 + x = -25.265259415 Solving -25 + x = -25.265259415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -25.265259415 + 25 Combine like terms: -25 + 25 = 0 0 + x = -25.265259415 + 25 x = -25.265259415 + 25 Combine like terms: -25.265259415 + 25 = -0.265259415 x = -0.265259415 Simplifying x = -0.265259415Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.265259415, -0.265259415}
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