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Simplifying -5x2 + 350x + -1750 = 0 Reorder the terms: -1750 + 350x + -5x2 = 0 Solving -1750 + 350x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-350 + 70x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-350 + 70x + -1x2)' equal to zero and attempt to solve: Simplifying -350 + 70x + -1x2 = 0 Solving -350 + 70x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 350 + -70x + x2 = 0 Move the constant term to the right: Add '-350' to each side of the equation. 350 + -70x + -350 + x2 = 0 + -350 Reorder the terms: 350 + -350 + -70x + x2 = 0 + -350 Combine like terms: 350 + -350 = 0 0 + -70x + x2 = 0 + -350 -70x + x2 = 0 + -350 Combine like terms: 0 + -350 = -350 -70x + x2 = -350 The x term is -70x. Take half its coefficient (-35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. -70x + 1225 + x2 = -350 + 1225 Reorder the terms: 1225 + -70x + x2 = -350 + 1225 Combine like terms: -350 + 1225 = 875 1225 + -70x + x2 = 875 Factor a perfect square on the left side: (x + -35)(x + -35) = 875 Calculate the square root of the right side: 29.580398915 Break this problem into two subproblems by setting (x + -35) equal to 29.580398915 and -29.580398915.Subproblem 1
x + -35 = 29.580398915 Simplifying x + -35 = 29.580398915 Reorder the terms: -35 + x = 29.580398915 Solving -35 + x = 29.580398915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = 29.580398915 + 35 Combine like terms: -35 + 35 = 0 0 + x = 29.580398915 + 35 x = 29.580398915 + 35 Combine like terms: 29.580398915 + 35 = 64.580398915 x = 64.580398915 Simplifying x = 64.580398915Subproblem 2
x + -35 = -29.580398915 Simplifying x + -35 = -29.580398915 Reorder the terms: -35 + x = -29.580398915 Solving -35 + x = -29.580398915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = -29.580398915 + 35 Combine like terms: -35 + 35 = 0 0 + x = -29.580398915 + 35 x = -29.580398915 + 35 Combine like terms: -29.580398915 + 35 = 5.419601085 x = 5.419601085 Simplifying x = 5.419601085Solution
The solution to the problem is based on the solutions from the subproblems. x = {64.580398915, 5.419601085}Solution
x = {64.580398915, 5.419601085}
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