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Simplifying 75x2 + 15600x + -100 = 0 Reorder the terms: -100 + 15600x + 75x2 = 0 Solving -100 + 15600x + 75x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '25'. 25(-4 + 624x + 3x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(-4 + 624x + 3x2)' equal to zero and attempt to solve: Simplifying -4 + 624x + 3x2 = 0 Solving -4 + 624x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + 208x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 208x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 208x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 208x + x2 = 0 + 1.333333333 208x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 208x + x2 = 1.333333333 The x term is 208x. Take half its coefficient (104). Square it (10816) and add it to both sides. Add '10816' to each side of the equation. 208x + 10816 + x2 = 1.333333333 + 10816 Reorder the terms: 10816 + 208x + x2 = 1.333333333 + 10816 Combine like terms: 1.333333333 + 10816 = 10817.333333333 10816 + 208x + x2 = 10817.333333333 Factor a perfect square on the left side: (x + 104)(x + 104) = 10817.333333333 Calculate the square root of the right side: 104.006410059 Break this problem into two subproblems by setting (x + 104) equal to 104.006410059 and -104.006410059.Subproblem 1
x + 104 = 104.006410059 Simplifying x + 104 = 104.006410059 Reorder the terms: 104 + x = 104.006410059 Solving 104 + x = 104.006410059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-104' to each side of the equation. 104 + -104 + x = 104.006410059 + -104 Combine like terms: 104 + -104 = 0 0 + x = 104.006410059 + -104 x = 104.006410059 + -104 Combine like terms: 104.006410059 + -104 = 0.006410059 x = 0.006410059 Simplifying x = 0.006410059Subproblem 2
x + 104 = -104.006410059 Simplifying x + 104 = -104.006410059 Reorder the terms: 104 + x = -104.006410059 Solving 104 + x = -104.006410059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-104' to each side of the equation. 104 + -104 + x = -104.006410059 + -104 Combine like terms: 104 + -104 = 0 0 + x = -104.006410059 + -104 x = -104.006410059 + -104 Combine like terms: -104.006410059 + -104 = -208.006410059 x = -208.006410059 Simplifying x = -208.006410059Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.006410059, -208.006410059}Solution
x = {0.006410059, -208.006410059}
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