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Simplifying 5000 + -700x + 20x2 = 6000 Solving 5000 + -700x + 20x2 = 6000 Solving for variable 'x'. Reorder the terms: 5000 + -6000 + -700x + 20x2 = 6000 + -6000 Combine like terms: 5000 + -6000 = -1000 -1000 + -700x + 20x2 = 6000 + -6000 Combine like terms: 6000 + -6000 = 0 -1000 + -700x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '20'. 20(-50 + -35x + x2) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(-50 + -35x + x2)' equal to zero and attempt to solve: Simplifying -50 + -35x + x2 = 0 Solving -50 + -35x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -35x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -35x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -35x + x2 = 0 + 50 -35x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -35x + x2 = 50 The x term is -35x. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35x + 306.25 + x2 = 50 + 306.25 Reorder the terms: 306.25 + -35x + x2 = 50 + 306.25 Combine like terms: 50 + 306.25 = 356.25 306.25 + -35x + x2 = 356.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 356.25 Calculate the square root of the right side: 18.874586088 Break this problem into two subproblems by setting (x + -17.5) equal to 18.874586088 and -18.874586088.Subproblem 1
x + -17.5 = 18.874586088 Simplifying x + -17.5 = 18.874586088 Reorder the terms: -17.5 + x = 18.874586088 Solving -17.5 + x = 18.874586088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = 18.874586088 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 18.874586088 + 17.5 x = 18.874586088 + 17.5 Combine like terms: 18.874586088 + 17.5 = 36.374586088 x = 36.374586088 Simplifying x = 36.374586088Subproblem 2
x + -17.5 = -18.874586088 Simplifying x + -17.5 = -18.874586088 Reorder the terms: -17.5 + x = -18.874586088 Solving -17.5 + x = -18.874586088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = -18.874586088 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -18.874586088 + 17.5 x = -18.874586088 + 17.5 Combine like terms: -18.874586088 + 17.5 = -1.374586088 x = -1.374586088 Simplifying x = -1.374586088Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.374586088, -1.374586088}Solution
x = {36.374586088, -1.374586088}
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