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Simplifying 0.3x2 + -140x + 2500 = 0 Reorder the terms: 2500 + -140x + 0.3x2 = 0 Solving 2500 + -140x + 0.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. 8333.333333 + -466.6666667x + x2 = 0 Move the constant term to the right: Add '-8333.333333' to each side of the equation. 8333.333333 + -466.6666667x + -8333.333333 + x2 = 0 + -8333.333333 Reorder the terms: 8333.333333 + -8333.333333 + -466.6666667x + x2 = 0 + -8333.333333 Combine like terms: 8333.333333 + -8333.333333 = 0.000000 0.000000 + -466.6666667x + x2 = 0 + -8333.333333 -466.6666667x + x2 = 0 + -8333.333333 Combine like terms: 0 + -8333.333333 = -8333.333333 -466.6666667x + x2 = -8333.333333 The x term is -466.6666667x. Take half its coefficient (-233.3333334). Square it (54444.44448) and add it to both sides. Add '54444.44448' to each side of the equation. -466.6666667x + 54444.44448 + x2 = -8333.333333 + 54444.44448 Reorder the terms: 54444.44448 + -466.6666667x + x2 = -8333.333333 + 54444.44448 Combine like terms: -8333.333333 + 54444.44448 = 46111.111147 54444.44448 + -466.6666667x + x2 = 46111.111147 Factor a perfect square on the left side: (x + -233.3333334)(x + -233.3333334) = 46111.111147 Calculate the square root of the right side: 214.734978862 Break this problem into two subproblems by setting (x + -233.3333334) equal to 214.734978862 and -214.734978862.Subproblem 1
x + -233.3333334 = 214.734978862 Simplifying x + -233.3333334 = 214.734978862 Reorder the terms: -233.3333334 + x = 214.734978862 Solving -233.3333334 + x = 214.734978862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '233.3333334' to each side of the equation. -233.3333334 + 233.3333334 + x = 214.734978862 + 233.3333334 Combine like terms: -233.3333334 + 233.3333334 = 0.0000000 0.0000000 + x = 214.734978862 + 233.3333334 x = 214.734978862 + 233.3333334 Combine like terms: 214.734978862 + 233.3333334 = 448.068312262 x = 448.068312262 Simplifying x = 448.068312262Subproblem 2
x + -233.3333334 = -214.734978862 Simplifying x + -233.3333334 = -214.734978862 Reorder the terms: -233.3333334 + x = -214.734978862 Solving -233.3333334 + x = -214.734978862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '233.3333334' to each side of the equation. -233.3333334 + 233.3333334 + x = -214.734978862 + 233.3333334 Combine like terms: -233.3333334 + 233.3333334 = 0.0000000 0.0000000 + x = -214.734978862 + 233.3333334 x = -214.734978862 + 233.3333334 Combine like terms: -214.734978862 + 233.3333334 = 18.598354538 x = 18.598354538 Simplifying x = 18.598354538Solution
The solution to the problem is based on the solutions from the subproblems. x = {448.068312262, 18.598354538}
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