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Simplifying x2 + -20x = 5x + -13 + -1x2 Reorder the terms: -20x + x2 = 5x + -13 + -1x2 Reorder the terms: -20x + x2 = -13 + 5x + -1x2 Solving -20x + x2 = -13 + 5x + -1x2 Solving for variable 'x'. Reorder the terms: 13 + -20x + -5x + x2 + x2 = -13 + 5x + -1x2 + 13 + -5x + x2 Combine like terms: -20x + -5x = -25x 13 + -25x + x2 + x2 = -13 + 5x + -1x2 + 13 + -5x + x2 Combine like terms: x2 + x2 = 2x2 13 + -25x + 2x2 = -13 + 5x + -1x2 + 13 + -5x + x2 Reorder the terms: 13 + -25x + 2x2 = -13 + 13 + 5x + -5x + -1x2 + x2 Combine like terms: -13 + 13 = 0 13 + -25x + 2x2 = 0 + 5x + -5x + -1x2 + x2 13 + -25x + 2x2 = 5x + -5x + -1x2 + x2 Combine like terms: 5x + -5x = 0 13 + -25x + 2x2 = 0 + -1x2 + x2 13 + -25x + 2x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 13 + -25x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6.5 + -12.5x + x2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -12.5x + -6.5 + x2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -12.5x + x2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -12.5x + x2 = 0 + -6.5 -12.5x + x2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -12.5x + x2 = -6.5 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = -6.5 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = -6.5 + 39.0625 Combine like terms: -6.5 + 39.0625 = 32.5625 39.0625 + -12.5x + x2 = 32.5625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 32.5625 Calculate the square root of the right side: 5.706356105 Break this problem into two subproblems by setting (x + -6.25) equal to 5.706356105 and -5.706356105.Subproblem 1
x + -6.25 = 5.706356105 Simplifying x + -6.25 = 5.706356105 Reorder the terms: -6.25 + x = 5.706356105 Solving -6.25 + x = 5.706356105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 5.706356105 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 5.706356105 + 6.25 x = 5.706356105 + 6.25 Combine like terms: 5.706356105 + 6.25 = 11.956356105 x = 11.956356105 Simplifying x = 11.956356105Subproblem 2
x + -6.25 = -5.706356105 Simplifying x + -6.25 = -5.706356105 Reorder the terms: -6.25 + x = -5.706356105 Solving -6.25 + x = -5.706356105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -5.706356105 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -5.706356105 + 6.25 x = -5.706356105 + 6.25 Combine like terms: -5.706356105 + 6.25 = 0.543643895 x = 0.543643895 Simplifying x = 0.543643895Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.956356105, 0.543643895}
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