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Simplifying -4x2 + 305x + -600 = 0 Reorder the terms: -600 + 305x + -4x2 = 0 Solving -600 + 305x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 150 + -76.25x + x2 = 0 Move the constant term to the right: Add '-150' to each side of the equation. 150 + -76.25x + -150 + x2 = 0 + -150 Reorder the terms: 150 + -150 + -76.25x + x2 = 0 + -150 Combine like terms: 150 + -150 = 0 0 + -76.25x + x2 = 0 + -150 -76.25x + x2 = 0 + -150 Combine like terms: 0 + -150 = -150 -76.25x + x2 = -150 The x term is -76.25x. Take half its coefficient (-38.125). Square it (1453.515625) and add it to both sides. Add '1453.515625' to each side of the equation. -76.25x + 1453.515625 + x2 = -150 + 1453.515625 Reorder the terms: 1453.515625 + -76.25x + x2 = -150 + 1453.515625 Combine like terms: -150 + 1453.515625 = 1303.515625 1453.515625 + -76.25x + x2 = 1303.515625 Factor a perfect square on the left side: (x + -38.125)(x + -38.125) = 1303.515625 Calculate the square root of the right side: 36.104232785 Break this problem into two subproblems by setting (x + -38.125) equal to 36.104232785 and -36.104232785.Subproblem 1
x + -38.125 = 36.104232785 Simplifying x + -38.125 = 36.104232785 Reorder the terms: -38.125 + x = 36.104232785 Solving -38.125 + x = 36.104232785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.125' to each side of the equation. -38.125 + 38.125 + x = 36.104232785 + 38.125 Combine like terms: -38.125 + 38.125 = 0.000 0.000 + x = 36.104232785 + 38.125 x = 36.104232785 + 38.125 Combine like terms: 36.104232785 + 38.125 = 74.229232785 x = 74.229232785 Simplifying x = 74.229232785Subproblem 2
x + -38.125 = -36.104232785 Simplifying x + -38.125 = -36.104232785 Reorder the terms: -38.125 + x = -36.104232785 Solving -38.125 + x = -36.104232785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.125' to each side of the equation. -38.125 + 38.125 + x = -36.104232785 + 38.125 Combine like terms: -38.125 + 38.125 = 0.000 0.000 + x = -36.104232785 + 38.125 x = -36.104232785 + 38.125 Combine like terms: -36.104232785 + 38.125 = 2.020767215 x = 2.020767215 Simplifying x = 2.020767215Solution
The solution to the problem is based on the solutions from the subproblems. x = {74.229232785, 2.020767215}
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