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Simplifying 0 = 3x2 + -150x + 1250 Reorder the terms: 0 = 1250 + -150x + 3x2 Solving 0 = 1250 + -150x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -1250 = -1250 -1250 + 150x + -3x2 = 1250 + -150x + 3x2 + -1250 + 150x + -3x2 Reorder the terms: -1250 + 150x + -3x2 = 1250 + -1250 + -150x + 150x + 3x2 + -3x2 Combine like terms: 1250 + -1250 = 0 -1250 + 150x + -3x2 = 0 + -150x + 150x + 3x2 + -3x2 -1250 + 150x + -3x2 = -150x + 150x + 3x2 + -3x2 Combine like terms: -150x + 150x = 0 -1250 + 150x + -3x2 = 0 + 3x2 + -3x2 -1250 + 150x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -1250 + 150x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 416.6666667 + -50x + x2 = 0 Move the constant term to the right: Add '-416.6666667' to each side of the equation. 416.6666667 + -50x + -416.6666667 + x2 = 0 + -416.6666667 Reorder the terms: 416.6666667 + -416.6666667 + -50x + x2 = 0 + -416.6666667 Combine like terms: 416.6666667 + -416.6666667 = 0.0000000 0.0000000 + -50x + x2 = 0 + -416.6666667 -50x + x2 = 0 + -416.6666667 Combine like terms: 0 + -416.6666667 = -416.6666667 -50x + x2 = -416.6666667 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 = -416.6666667 + 625 Reorder the terms: 625 + -50x + x2 = -416.6666667 + 625 Combine like terms: -416.6666667 + 625 = 208.3333333 625 + -50x + x2 = 208.3333333 Factor a perfect square on the left side: (x + -25)(x + -25) = 208.3333333 Calculate the square root of the right side: 14.433756729 Break this problem into two subproblems by setting (x + -25) equal to 14.433756729 and -14.433756729.Subproblem 1
x + -25 = 14.433756729 Simplifying x + -25 = 14.433756729 Reorder the terms: -25 + x = 14.433756729 Solving -25 + x = 14.433756729 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 = 14.433756729 + 25 Combine like terms: -25 + 25 = 0 0 + x = 14.433756729 + 25 x = 14.433756729 + 25 Combine like terms: 14.433756729 + 25 = 39.433756729 x = 39.433756729 Simplifying x = 39.433756729Subproblem 2
x + -25 = -14.433756729 Simplifying x + -25 = -14.433756729 Reorder the terms: -25 + x = -14.433756729 Solving -25 + x = -14.433756729 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 = -14.433756729 + 25 Combine like terms: -25 + 25 = 0 0 + x = -14.433756729 + 25 x = -14.433756729 + 25 Combine like terms: -14.433756729 + 25 = 10.566243271 x = 10.566243271 Simplifying x = 10.566243271Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.433756729, 10.566243271}
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