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Simplifying 320x + 1538 = 16x2 Reorder the terms: 1538 + 320x = 16x2 Solving 1538 + 320x = 16x2 Solving for variable 'x'. Combine like terms: 16x2 + -16x2 = 0 1538 + 320x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(769 + 160x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(769 + 160x + -8x2)' equal to zero and attempt to solve: Simplifying 769 + 160x + -8x2 = 0 Solving 769 + 160x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -96.125 + -20x + x2 = 0 Move the constant term to the right: Add '96.125' to each side of the equation. -96.125 + -20x + 96.125 + x2 = 0 + 96.125 Reorder the terms: -96.125 + 96.125 + -20x + x2 = 0 + 96.125 Combine like terms: -96.125 + 96.125 = 0.000 0.000 + -20x + x2 = 0 + 96.125 -20x + x2 = 0 + 96.125 Combine like terms: 0 + 96.125 = 96.125 -20x + x2 = 96.125 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 96.125 + 100 Reorder the terms: 100 + -20x + x2 = 96.125 + 100 Combine like terms: 96.125 + 100 = 196.125 100 + -20x + x2 = 196.125 Factor a perfect square on the left side: (x + -10)(x + -10) = 196.125 Calculate the square root of the right side: 14.004463574 Break this problem into two subproblems by setting (x + -10) equal to 14.004463574 and -14.004463574.Subproblem 1
x + -10 = 14.004463574 Simplifying x + -10 = 14.004463574 Reorder the terms: -10 + x = 14.004463574 Solving -10 + x = 14.004463574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 14.004463574 + 10 Combine like terms: -10 + 10 = 0 0 + x = 14.004463574 + 10 x = 14.004463574 + 10 Combine like terms: 14.004463574 + 10 = 24.004463574 x = 24.004463574 Simplifying x = 24.004463574Subproblem 2
x + -10 = -14.004463574 Simplifying x + -10 = -14.004463574 Reorder the terms: -10 + x = -14.004463574 Solving -10 + x = -14.004463574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -14.004463574 + 10 Combine like terms: -10 + 10 = 0 0 + x = -14.004463574 + 10 x = -14.004463574 + 10 Combine like terms: -14.004463574 + 10 = -4.004463574 x = -4.004463574 Simplifying x = -4.004463574Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.004463574, -4.004463574}Solution
x = {24.004463574, -4.004463574}
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