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Simplifying 50x2 + 275x + -450 = 0 Reorder the terms: -450 + 275x + 50x2 = 0 Solving -450 + 275x + 50x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '25'. 25(-18 + 11x + 2x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(-18 + 11x + 2x2)' equal to zero and attempt to solve: Simplifying -18 + 11x + 2x2 = 0 Solving -18 + 11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9 + 5.5x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 5.5x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 5.5x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 5.5x + x2 = 0 + 9 5.5x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 5.5x + x2 = 9 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 9 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 9 + 7.5625 Combine like terms: 9 + 7.5625 = 16.5625 7.5625 + 5.5x + x2 = 16.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 16.5625 Calculate the square root of the right side: 4.069705149 Break this problem into two subproblems by setting (x + 2.75) equal to 4.069705149 and -4.069705149.Subproblem 1
x + 2.75 = 4.069705149 Simplifying x + 2.75 = 4.069705149 Reorder the terms: 2.75 + x = 4.069705149 Solving 2.75 + x = 4.069705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 4.069705149 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 4.069705149 + -2.75 x = 4.069705149 + -2.75 Combine like terms: 4.069705149 + -2.75 = 1.319705149 x = 1.319705149 Simplifying x = 1.319705149Subproblem 2
x + 2.75 = -4.069705149 Simplifying x + 2.75 = -4.069705149 Reorder the terms: 2.75 + x = -4.069705149 Solving 2.75 + x = -4.069705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -4.069705149 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -4.069705149 + -2.75 x = -4.069705149 + -2.75 Combine like terms: -4.069705149 + -2.75 = -6.819705149 x = -6.819705149 Simplifying x = -6.819705149Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.319705149, -6.819705149}Solution
x = {1.319705149, -6.819705149}
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