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Simplifying 4x2 + 34x + -20 = 0 Reorder the terms: -20 + 34x + 4x2 = 0 Solving -20 + 34x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + 17x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + 17x + 2x2)' equal to zero and attempt to solve: Simplifying -10 + 17x + 2x2 = 0 Solving -10 + 17x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5 + 8.5x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 8.5x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 8.5x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 8.5x + x2 = 0 + 5 8.5x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 8.5x + x2 = 5 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = 5 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 5 + 18.0625 Combine like terms: 5 + 18.0625 = 23.0625 18.0625 + 8.5x + x2 = 23.0625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 23.0625 Calculate the square root of the right side: 4.802343178 Break this problem into two subproblems by setting (x + 4.25) equal to 4.802343178 and -4.802343178.Subproblem 1
x + 4.25 = 4.802343178 Simplifying x + 4.25 = 4.802343178 Reorder the terms: 4.25 + x = 4.802343178 Solving 4.25 + x = 4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 4.802343178 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 4.802343178 + -4.25 x = 4.802343178 + -4.25 Combine like terms: 4.802343178 + -4.25 = 0.552343178 x = 0.552343178 Simplifying x = 0.552343178Subproblem 2
x + 4.25 = -4.802343178 Simplifying x + 4.25 = -4.802343178 Reorder the terms: 4.25 + x = -4.802343178 Solving 4.25 + x = -4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -4.802343178 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -4.802343178 + -4.25 x = -4.802343178 + -4.25 Combine like terms: -4.802343178 + -4.25 = -9.052343178 x = -9.052343178 Simplifying x = -9.052343178Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.552343178, -9.052343178}Solution
x = {0.552343178, -9.052343178}
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