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Simplifying 2x2 + -20x + 9 = 0 Reorder the terms: 9 + -20x + 2x2 = 0 Solving 9 + -20x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + -10x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -10x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -10x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -10x + x2 = 0 + -4.5 -10x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -10x + x2 = -4.5 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -4.5 + 25 Reorder the terms: 25 + -10x + x2 = -4.5 + 25 Combine like terms: -4.5 + 25 = 20.5 25 + -10x + x2 = 20.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 20.5 Calculate the square root of the right side: 4.527692569 Break this problem into two subproblems by setting (x + -5) equal to 4.527692569 and -4.527692569.Subproblem 1
x + -5 = 4.527692569 Simplifying x + -5 = 4.527692569 Reorder the terms: -5 + x = 4.527692569 Solving -5 + x = 4.527692569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.527692569 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.527692569 + 5 x = 4.527692569 + 5 Combine like terms: 4.527692569 + 5 = 9.527692569 x = 9.527692569 Simplifying x = 9.527692569Subproblem 2
x + -5 = -4.527692569 Simplifying x + -5 = -4.527692569 Reorder the terms: -5 + x = -4.527692569 Solving -5 + x = -4.527692569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.527692569 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.527692569 + 5 x = -4.527692569 + 5 Combine like terms: -4.527692569 + 5 = 0.472307431 x = 0.472307431 Simplifying x = 0.472307431Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.527692569, 0.472307431}
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