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Simplifying 4x2 + 136x + -450 = 0 Reorder the terms: -450 + 136x + 4x2 = 0 Solving -450 + 136x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-225 + 68x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-225 + 68x + 2x2)' equal to zero and attempt to solve: Simplifying -225 + 68x + 2x2 = 0 Solving -225 + 68x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -112.5 + 34x + x2 = 0 Move the constant term to the right: Add '112.5' to each side of the equation. -112.5 + 34x + 112.5 + x2 = 0 + 112.5 Reorder the terms: -112.5 + 112.5 + 34x + x2 = 0 + 112.5 Combine like terms: -112.5 + 112.5 = 0.0 0.0 + 34x + x2 = 0 + 112.5 34x + x2 = 0 + 112.5 Combine like terms: 0 + 112.5 = 112.5 34x + x2 = 112.5 The x term is 34x. Take half its coefficient (17). Square it (289) and add it to both sides. Add '289' to each side of the equation. 34x + 289 + x2 = 112.5 + 289 Reorder the terms: 289 + 34x + x2 = 112.5 + 289 Combine like terms: 112.5 + 289 = 401.5 289 + 34x + x2 = 401.5 Factor a perfect square on the left side: (x + 17)(x + 17) = 401.5 Calculate the square root of the right side: 20.03746491 Break this problem into two subproblems by setting (x + 17) equal to 20.03746491 and -20.03746491.Subproblem 1
x + 17 = 20.03746491 Simplifying x + 17 = 20.03746491 Reorder the terms: 17 + x = 20.03746491 Solving 17 + x = 20.03746491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = 20.03746491 + -17 Combine like terms: 17 + -17 = 0 0 + x = 20.03746491 + -17 x = 20.03746491 + -17 Combine like terms: 20.03746491 + -17 = 3.03746491 x = 3.03746491 Simplifying x = 3.03746491Subproblem 2
x + 17 = -20.03746491 Simplifying x + 17 = -20.03746491 Reorder the terms: 17 + x = -20.03746491 Solving 17 + x = -20.03746491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = -20.03746491 + -17 Combine like terms: 17 + -17 = 0 0 + x = -20.03746491 + -17 x = -20.03746491 + -17 Combine like terms: -20.03746491 + -17 = -37.03746491 x = -37.03746491 Simplifying x = -37.03746491Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.03746491, -37.03746491}Solution
x = {3.03746491, -37.03746491}
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