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Simplifying 0 = x2 + -20x + -35 Reorder the terms: 0 = -35 + -20x + x2 Solving 0 = -35 + -20x + x2 Solving for variable 'x'. Combine like terms: 0 + 35 = 35 35 + 20x + -1x2 = -35 + -20x + x2 + 35 + 20x + -1x2 Reorder the terms: 35 + 20x + -1x2 = -35 + 35 + -20x + 20x + x2 + -1x2 Combine like terms: -35 + 35 = 0 35 + 20x + -1x2 = 0 + -20x + 20x + x2 + -1x2 35 + 20x + -1x2 = -20x + 20x + x2 + -1x2 Combine like terms: -20x + 20x = 0 35 + 20x + -1x2 = 0 + x2 + -1x2 35 + 20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 35 + 20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -35 + -20x + x2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + -20x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + -20x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -20x + x2 = 0 + 35 -20x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 -20x + x2 = 35 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 = 35 + 100 Reorder the terms: 100 + -20x + x2 = 35 + 100 Combine like terms: 35 + 100 = 135 100 + -20x + x2 = 135 Factor a perfect square on the left side: (x + -10)(x + -10) = 135 Calculate the square root of the right side: 11.618950039 Break this problem into two subproblems by setting (x + -10) equal to 11.618950039 and -11.618950039.Subproblem 1
x + -10 = 11.618950039 Simplifying x + -10 = 11.618950039 Reorder the terms: -10 + x = 11.618950039 Solving -10 + x = 11.618950039 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 = 11.618950039 + 10 Combine like terms: -10 + 10 = 0 0 + x = 11.618950039 + 10 x = 11.618950039 + 10 Combine like terms: 11.618950039 + 10 = 21.618950039 x = 21.618950039 Simplifying x = 21.618950039Subproblem 2
x + -10 = -11.618950039 Simplifying x + -10 = -11.618950039 Reorder the terms: -10 + x = -11.618950039 Solving -10 + x = -11.618950039 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 = -11.618950039 + 10 Combine like terms: -10 + 10 = 0 0 + x = -11.618950039 + 10 x = -11.618950039 + 10 Combine like terms: -11.618950039 + 10 = -1.618950039 x = -1.618950039 Simplifying x = -1.618950039Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.618950039, -1.618950039}
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