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Simplifying x2 + -20x + 10 = 0 Reorder the terms: 10 + -20x + x2 = 0 Solving 10 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -20x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -20x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -20x + x2 = 0 + -10 -20x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -20x + x2 = -10 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 = -10 + 100 Reorder the terms: 100 + -20x + x2 = -10 + 100 Combine like terms: -10 + 100 = 90 100 + -20x + x2 = 90 Factor a perfect square on the left side: (x + -10)(x + -10) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (x + -10) equal to 9.486832981 and -9.486832981.Subproblem 1
x + -10 = 9.486832981 Simplifying x + -10 = 9.486832981 Reorder the terms: -10 + x = 9.486832981 Solving -10 + x = 9.486832981 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 = 9.486832981 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.486832981 + 10 x = 9.486832981 + 10 Combine like terms: 9.486832981 + 10 = 19.486832981 x = 19.486832981 Simplifying x = 19.486832981Subproblem 2
x + -10 = -9.486832981 Simplifying x + -10 = -9.486832981 Reorder the terms: -10 + x = -9.486832981 Solving -10 + x = -9.486832981 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 = -9.486832981 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.486832981 + 10 x = -9.486832981 + 10 Combine like terms: -9.486832981 + 10 = 0.513167019 x = 0.513167019 Simplifying x = 0.513167019Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.486832981, 0.513167019}
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