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Simplifying 20x = x2 + 5 Reorder the terms: 20x = 5 + x2 Solving 20x = 5 + x2 Solving for variable 'x'. Reorder the terms: -5 + 20x + -1x2 = 5 + x2 + -5 + -1x2 Reorder the terms: -5 + 20x + -1x2 = 5 + -5 + x2 + -1x2 Combine like terms: 5 + -5 = 0 -5 + 20x + -1x2 = 0 + x2 + -1x2 -5 + 20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -5 + 20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5 + -20x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -20x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -20x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -20x + x2 = 0 + -5 -20x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -20x + x2 = -5 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 = -5 + 100 Reorder the terms: 100 + -20x + x2 = -5 + 100 Combine like terms: -5 + 100 = 95 100 + -20x + x2 = 95 Factor a perfect square on the left side: (x + -10)(x + -10) = 95 Calculate the square root of the right side: 9.746794345 Break this problem into two subproblems by setting (x + -10) equal to 9.746794345 and -9.746794345.Subproblem 1
x + -10 = 9.746794345 Simplifying x + -10 = 9.746794345 Reorder the terms: -10 + x = 9.746794345 Solving -10 + x = 9.746794345 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 = 9.746794345 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.746794345 + 10 x = 9.746794345 + 10 Combine like terms: 9.746794345 + 10 = 19.746794345 x = 19.746794345 Simplifying x = 19.746794345Subproblem 2
x + -10 = -9.746794345 Simplifying x + -10 = -9.746794345 Reorder the terms: -10 + x = -9.746794345 Solving -10 + x = -9.746794345 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 = -9.746794345 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.746794345 + 10 x = -9.746794345 + 10 Combine like terms: -9.746794345 + 10 = 0.253205655 x = 0.253205655 Simplifying x = 0.253205655Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.746794345, 0.253205655}
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