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Simplifying 20x2 + 200x + -700 = 0 Reorder the terms: -700 + 200x + 20x2 = 0 Solving -700 + 200x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '20'. 20(-35 + 10x + x2) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(-35 + 10x + x2)' equal to zero and attempt to solve: Simplifying -35 + 10x + x2 = 0 Solving -35 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + 10x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + 10x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 10x + x2 = 0 + 35 10x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 10x + x2 = 35 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 35 + 25 Reorder the terms: 25 + 10x + x2 = 35 + 25 Combine like terms: 35 + 25 = 60 25 + 10x + x2 = 60 Factor a perfect square on the left side: (x + 5)(x + 5) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + 5) equal to 7.745966692 and -7.745966692.Subproblem 1
x + 5 = 7.745966692 Simplifying x + 5 = 7.745966692 Reorder the terms: 5 + x = 7.745966692 Solving 5 + x = 7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 7.745966692 + -5 Combine like terms: 5 + -5 = 0 0 + x = 7.745966692 + -5 x = 7.745966692 + -5 Combine like terms: 7.745966692 + -5 = 2.745966692 x = 2.745966692 Simplifying x = 2.745966692Subproblem 2
x + 5 = -7.745966692 Simplifying x + 5 = -7.745966692 Reorder the terms: 5 + x = -7.745966692 Solving 5 + x = -7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -7.745966692 + -5 Combine like terms: 5 + -5 = 0 0 + x = -7.745966692 + -5 x = -7.745966692 + -5 Combine like terms: -7.745966692 + -5 = -12.745966692 x = -12.745966692 Simplifying x = -12.745966692Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.745966692, -12.745966692}Solution
x = {2.745966692, -12.745966692}
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