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Simplifying 50x2 + -594x + 1620 = 0 Reorder the terms: 1620 + -594x + 50x2 = 0 Solving 1620 + -594x + 50x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(810 + -297x + 25x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(810 + -297x + 25x2)' equal to zero and attempt to solve: Simplifying 810 + -297x + 25x2 = 0 Solving 810 + -297x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 32.4 + -11.88x + x2 = 0 Move the constant term to the right: Add '-32.4' to each side of the equation. 32.4 + -11.88x + -32.4 + x2 = 0 + -32.4 Reorder the terms: 32.4 + -32.4 + -11.88x + x2 = 0 + -32.4 Combine like terms: 32.4 + -32.4 = 0.0 0.0 + -11.88x + x2 = 0 + -32.4 -11.88x + x2 = 0 + -32.4 Combine like terms: 0 + -32.4 = -32.4 -11.88x + x2 = -32.4 The x term is -11.88x. Take half its coefficient (-5.94). Square it (35.2836) and add it to both sides. Add '35.2836' to each side of the equation. -11.88x + 35.2836 + x2 = -32.4 + 35.2836 Reorder the terms: 35.2836 + -11.88x + x2 = -32.4 + 35.2836 Combine like terms: -32.4 + 35.2836 = 2.8836 35.2836 + -11.88x + x2 = 2.8836 Factor a perfect square on the left side: (x + -5.94)(x + -5.94) = 2.8836 Calculate the square root of the right side: 1.698116604 Break this problem into two subproblems by setting (x + -5.94) equal to 1.698116604 and -1.698116604.Subproblem 1
x + -5.94 = 1.698116604 Simplifying x + -5.94 = 1.698116604 Reorder the terms: -5.94 + x = 1.698116604 Solving -5.94 + x = 1.698116604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.94' to each side of the equation. -5.94 + 5.94 + x = 1.698116604 + 5.94 Combine like terms: -5.94 + 5.94 = 0.00 0.00 + x = 1.698116604 + 5.94 x = 1.698116604 + 5.94 Combine like terms: 1.698116604 + 5.94 = 7.638116604 x = 7.638116604 Simplifying x = 7.638116604Subproblem 2
x + -5.94 = -1.698116604 Simplifying x + -5.94 = -1.698116604 Reorder the terms: -5.94 + x = -1.698116604 Solving -5.94 + x = -1.698116604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.94' to each side of the equation. -5.94 + 5.94 + x = -1.698116604 + 5.94 Combine like terms: -5.94 + 5.94 = 0.00 0.00 + x = -1.698116604 + 5.94 x = -1.698116604 + 5.94 Combine like terms: -1.698116604 + 5.94 = 4.241883396 x = 4.241883396 Simplifying x = 4.241883396Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.638116604, 4.241883396}Solution
x = {7.638116604, 4.241883396}
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