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Simplifying 2x2 + 102x + 289 = 0 Reorder the terms: 289 + 102x + 2x2 = 0 Solving 289 + 102x + 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'. 144.5 + 51x + x2 = 0 Move the constant term to the right: Add '-144.5' to each side of the equation. 144.5 + 51x + -144.5 + x2 = 0 + -144.5 Reorder the terms: 144.5 + -144.5 + 51x + x2 = 0 + -144.5 Combine like terms: 144.5 + -144.5 = 0.0 0.0 + 51x + x2 = 0 + -144.5 51x + x2 = 0 + -144.5 Combine like terms: 0 + -144.5 = -144.5 51x + x2 = -144.5 The x term is 51x. Take half its coefficient (25.5). Square it (650.25) and add it to both sides. Add '650.25' to each side of the equation. 51x + 650.25 + x2 = -144.5 + 650.25 Reorder the terms: 650.25 + 51x + x2 = -144.5 + 650.25 Combine like terms: -144.5 + 650.25 = 505.75 650.25 + 51x + x2 = 505.75 Factor a perfect square on the left side: (x + 25.5)(x + 25.5) = 505.75 Calculate the square root of the right side: 22.488886144 Break this problem into two subproblems by setting (x + 25.5) equal to 22.488886144 and -22.488886144.Subproblem 1
x + 25.5 = 22.488886144 Simplifying x + 25.5 = 22.488886144 Reorder the terms: 25.5 + x = 22.488886144 Solving 25.5 + x = 22.488886144 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25.5' to each side of the equation. 25.5 + -25.5 + x = 22.488886144 + -25.5 Combine like terms: 25.5 + -25.5 = 0.0 0.0 + x = 22.488886144 + -25.5 x = 22.488886144 + -25.5 Combine like terms: 22.488886144 + -25.5 = -3.011113856 x = -3.011113856 Simplifying x = -3.011113856Subproblem 2
x + 25.5 = -22.488886144 Simplifying x + 25.5 = -22.488886144 Reorder the terms: 25.5 + x = -22.488886144 Solving 25.5 + x = -22.488886144 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25.5' to each side of the equation. 25.5 + -25.5 + x = -22.488886144 + -25.5 Combine like terms: 25.5 + -25.5 = 0.0 0.0 + x = -22.488886144 + -25.5 x = -22.488886144 + -25.5 Combine like terms: -22.488886144 + -25.5 = -47.988886144 x = -47.988886144 Simplifying x = -47.988886144Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.011113856, -47.988886144}
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