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Simplifying 10x2 + 10x + -208 = 0 Reorder the terms: -208 + 10x + 10x2 = 0 Solving -208 + 10x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-104 + 5x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-104 + 5x + 5x2)' equal to zero and attempt to solve: Simplifying -104 + 5x + 5x2 = 0 Solving -104 + 5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -20.8 + x + x2 = 0 Move the constant term to the right: Add '20.8' to each side of the equation. -20.8 + x + 20.8 + x2 = 0 + 20.8 Reorder the terms: -20.8 + 20.8 + x + x2 = 0 + 20.8 Combine like terms: -20.8 + 20.8 = 0.0 0.0 + x + x2 = 0 + 20.8 x + x2 = 0 + 20.8 Combine like terms: 0 + 20.8 = 20.8 x + x2 = 20.8 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 20.8 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 20.8 + 0.25 Combine like terms: 20.8 + 0.25 = 21.05 1.25 + x2 = 21.05 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 21.05 Calculate the square root of the right side: 4.588027899 Break this problem into two subproblems by setting (x + 0.5) equal to 4.588027899 and -4.588027899.Subproblem 1
x + 0.5 = 4.588027899 Simplifying x + 0.5 = 4.588027899 Reorder the terms: 0.5 + x = 4.588027899 Solving 0.5 + x = 4.588027899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.588027899 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.588027899 + -0.5 x = 4.588027899 + -0.5 Combine like terms: 4.588027899 + -0.5 = 4.088027899 x = 4.088027899 Simplifying x = 4.088027899Subproblem 2
x + 0.5 = -4.588027899 Simplifying x + 0.5 = -4.588027899 Reorder the terms: 0.5 + x = -4.588027899 Solving 0.5 + x = -4.588027899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.588027899 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.588027899 + -0.5 x = -4.588027899 + -0.5 Combine like terms: -4.588027899 + -0.5 = -5.088027899 x = -5.088027899 Simplifying x = -5.088027899Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.088027899, -5.088027899}Solution
x = {4.088027899, -5.088027899}
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