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Simplifying 50x2 + 50x + -1344 = 0 Reorder the terms: -1344 + 50x + 50x2 = 0 Solving -1344 + 50x + 50x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-672 + 25x + 25x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-672 + 25x + 25x2)' equal to zero and attempt to solve: Simplifying -672 + 25x + 25x2 = 0 Solving -672 + 25x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -26.88 + x + x2 = 0 Move the constant term to the right: Add '26.88' to each side of the equation. -26.88 + x + 26.88 + x2 = 0 + 26.88 Reorder the terms: -26.88 + 26.88 + x + x2 = 0 + 26.88 Combine like terms: -26.88 + 26.88 = 0.00 0.00 + x + x2 = 0 + 26.88 x + x2 = 0 + 26.88 Combine like terms: 0 + 26.88 = 26.88 x + x2 = 26.88 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 = 26.88 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 26.88 + 0.25 Combine like terms: 26.88 + 0.25 = 27.13 1.25 + x2 = 27.13 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 27.13 Calculate the square root of the right side: 5.208646657 Break this problem into two subproblems by setting (x + 0.5) equal to 5.208646657 and -5.208646657.Subproblem 1
x + 0.5 = 5.208646657 Simplifying x + 0.5 = 5.208646657 Reorder the terms: 0.5 + x = 5.208646657 Solving 0.5 + x = 5.208646657 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 = 5.208646657 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.208646657 + -0.5 x = 5.208646657 + -0.5 Combine like terms: 5.208646657 + -0.5 = 4.708646657 x = 4.708646657 Simplifying x = 4.708646657Subproblem 2
x + 0.5 = -5.208646657 Simplifying x + 0.5 = -5.208646657 Reorder the terms: 0.5 + x = -5.208646657 Solving 0.5 + x = -5.208646657 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 = -5.208646657 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.208646657 + -0.5 x = -5.208646657 + -0.5 Combine like terms: -5.208646657 + -0.5 = -5.708646657 x = -5.708646657 Simplifying x = -5.708646657Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.708646657, -5.708646657}Solution
x = {4.708646657, -5.708646657}
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