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Simplifying 2x2 + 20x + 400 = 598 Reorder the terms: 400 + 20x + 2x2 = 598 Solving 400 + 20x + 2x2 = 598 Solving for variable 'x'. Reorder the terms: 400 + -598 + 20x + 2x2 = 598 + -598 Combine like terms: 400 + -598 = -198 -198 + 20x + 2x2 = 598 + -598 Combine like terms: 598 + -598 = 0 -198 + 20x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-99 + 10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-99 + 10x + x2)' equal to zero and attempt to solve: Simplifying -99 + 10x + x2 = 0 Solving -99 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + 10x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + 10x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + 10x + x2 = 0 + 99 10x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 10x + x2 = 99 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 = 99 + 25 Reorder the terms: 25 + 10x + x2 = 99 + 25 Combine like terms: 99 + 25 = 124 25 + 10x + x2 = 124 Factor a perfect square on the left side: (x + 5)(x + 5) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (x + 5) equal to 11.135528726 and -11.135528726.Subproblem 1
x + 5 = 11.135528726 Simplifying x + 5 = 11.135528726 Reorder the terms: 5 + x = 11.135528726 Solving 5 + x = 11.135528726 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 = 11.135528726 + -5 Combine like terms: 5 + -5 = 0 0 + x = 11.135528726 + -5 x = 11.135528726 + -5 Combine like terms: 11.135528726 + -5 = 6.135528726 x = 6.135528726 Simplifying x = 6.135528726Subproblem 2
x + 5 = -11.135528726 Simplifying x + 5 = -11.135528726 Reorder the terms: 5 + x = -11.135528726 Solving 5 + x = -11.135528726 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 = -11.135528726 + -5 Combine like terms: 5 + -5 = 0 0 + x = -11.135528726 + -5 x = -11.135528726 + -5 Combine like terms: -11.135528726 + -5 = -16.135528726 x = -16.135528726 Simplifying x = -16.135528726Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.135528726, -16.135528726}Solution
x = {6.135528726, -16.135528726}
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