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Simplifying x + 512 = 20x2 + 512x Reorder the terms: 512 + x = 20x2 + 512x Reorder the terms: 512 + x = 512x + 20x2 Solving 512 + x = 512x + 20x2 Solving for variable 'x'. Combine like terms: x + -512x = -511x 512 + -511x + -20x2 = 512x + 20x2 + -512x + -20x2 Reorder the terms: 512 + -511x + -20x2 = 512x + -512x + 20x2 + -20x2 Combine like terms: 512x + -512x = 0 512 + -511x + -20x2 = 0 + 20x2 + -20x2 512 + -511x + -20x2 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 512 + -511x + -20x2 = 0 Begin completing the square. Divide all terms by -20 the coefficient of the squared term: Divide each side by '-20'. -25.6 + 25.55x + x2 = 0 Move the constant term to the right: Add '25.6' to each side of the equation. -25.6 + 25.55x + 25.6 + x2 = 0 + 25.6 Reorder the terms: -25.6 + 25.6 + 25.55x + x2 = 0 + 25.6 Combine like terms: -25.6 + 25.6 = 0.0 0.0 + 25.55x + x2 = 0 + 25.6 25.55x + x2 = 0 + 25.6 Combine like terms: 0 + 25.6 = 25.6 25.55x + x2 = 25.6 The x term is 25.55x. Take half its coefficient (12.775). Square it (163.200625) and add it to both sides. Add '163.200625' to each side of the equation. 25.55x + 163.200625 + x2 = 25.6 + 163.200625 Reorder the terms: 163.200625 + 25.55x + x2 = 25.6 + 163.200625 Combine like terms: 25.6 + 163.200625 = 188.800625 163.200625 + 25.55x + x2 = 188.800625 Factor a perfect square on the left side: (x + 12.775)(x + 12.775) = 188.800625 Calculate the square root of the right side: 13.740473973 Break this problem into two subproblems by setting (x + 12.775) equal to 13.740473973 and -13.740473973.Subproblem 1
x + 12.775 = 13.740473973 Simplifying x + 12.775 = 13.740473973 Reorder the terms: 12.775 + x = 13.740473973 Solving 12.775 + x = 13.740473973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.775' to each side of the equation. 12.775 + -12.775 + x = 13.740473973 + -12.775 Combine like terms: 12.775 + -12.775 = 0.000 0.000 + x = 13.740473973 + -12.775 x = 13.740473973 + -12.775 Combine like terms: 13.740473973 + -12.775 = 0.965473973 x = 0.965473973 Simplifying x = 0.965473973Subproblem 2
x + 12.775 = -13.740473973 Simplifying x + 12.775 = -13.740473973 Reorder the terms: 12.775 + x = -13.740473973 Solving 12.775 + x = -13.740473973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.775' to each side of the equation. 12.775 + -12.775 + x = -13.740473973 + -12.775 Combine like terms: 12.775 + -12.775 = 0.000 0.000 + x = -13.740473973 + -12.775 x = -13.740473973 + -12.775 Combine like terms: -13.740473973 + -12.775 = -26.515473973 x = -26.515473973 Simplifying x = -26.515473973Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.965473973, -26.515473973}
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