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Simplifying 2x2 + -10x + 1 = 0 Reorder the terms: 1 + -10x + 2x2 = 0 Solving 1 + -10x + 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'. 0.5 + -5x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -5x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -5x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -5x + x2 = 0 + -0.5 -5x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -5x + x2 = -0.5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -0.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -0.5 + 6.25 Combine like terms: -0.5 + 6.25 = 5.75 6.25 + -5x + x2 = 5.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 5.75 Calculate the square root of the right side: 2.397915762 Break this problem into two subproblems by setting (x + -2.5) equal to 2.397915762 and -2.397915762.Subproblem 1
x + -2.5 = 2.397915762 Simplifying x + -2.5 = 2.397915762 Reorder the terms: -2.5 + x = 2.397915762 Solving -2.5 + x = 2.397915762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.397915762 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.397915762 + 2.5 x = 2.397915762 + 2.5 Combine like terms: 2.397915762 + 2.5 = 4.897915762 x = 4.897915762 Simplifying x = 4.897915762Subproblem 2
x + -2.5 = -2.397915762 Simplifying x + -2.5 = -2.397915762 Reorder the terms: -2.5 + x = -2.397915762 Solving -2.5 + x = -2.397915762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.397915762 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.397915762 + 2.5 x = -2.397915762 + 2.5 Combine like terms: -2.397915762 + 2.5 = 0.102084238 x = 0.102084238 Simplifying x = 0.102084238Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.897915762, 0.102084238}
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