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Simplifying 64.95 = (25 + -1x) + (3.12) + (x) * x(2.49) Remove parenthesis around (25 + -1x) 64.95 = 25 + -1x + (3.12) + (x) * x(2.49) 64.95 = 25 + -1x + 3.12 + (x) * x(2.49) Reorder the terms for easier multiplication: 64.95 = 25 + -1x + 3.12 + 2.49x * x Multiply x * x 64.95 = 25 + -1x + 3.12 + 2.49x2 Reorder the terms: 64.95 = 25 + 3.12 + -1x + 2.49x2 Combine like terms: 25 + 3.12 = 28.12 64.95 = 28.12 + -1x + 2.49x2 Solving 64.95 = 28.12 + -1x + 2.49x2 Solving for variable 'x'. Combine like terms: 64.95 + -28.12 = 36.83 36.83 + x + -2.49x2 = 28.12 + -1x + 2.49x2 + -28.12 + x + -2.49x2 Reorder the terms: 36.83 + x + -2.49x2 = 28.12 + -28.12 + -1x + x + 2.49x2 + -2.49x2 Combine like terms: 28.12 + -28.12 = 0.00 36.83 + x + -2.49x2 = 0.00 + -1x + x + 2.49x2 + -2.49x2 36.83 + x + -2.49x2 = -1x + x + 2.49x2 + -2.49x2 Combine like terms: -1x + x = 0 36.83 + x + -2.49x2 = 0 + 2.49x2 + -2.49x2 36.83 + x + -2.49x2 = 2.49x2 + -2.49x2 Combine like terms: 2.49x2 + -2.49x2 = 0.00 36.83 + x + -2.49x2 = 0.00 Begin completing the square. Divide all terms by -2.49 the coefficient of the squared term: Divide each side by '-2.49'. -14.79116466 + -0.4016064257x + x2 = 0 Move the constant term to the right: Add '14.79116466' to each side of the equation. -14.79116466 + -0.4016064257x + 14.79116466 + x2 = 0 + 14.79116466 Reorder the terms: -14.79116466 + 14.79116466 + -0.4016064257x + x2 = 0 + 14.79116466 Combine like terms: -14.79116466 + 14.79116466 = 0.00000000 0.00000000 + -0.4016064257x + x2 = 0 + 14.79116466 -0.4016064257x + x2 = 0 + 14.79116466 Combine like terms: 0 + 14.79116466 = 14.79116466 -0.4016064257x + x2 = 14.79116466 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.4016064257x + 0.25 + x2 = 14.79116466 + 0.25 Reorder the terms: 0.25 + -0.4016064257x + x2 = 14.79116466 + 0.25 Combine like terms: 14.79116466 + 0.25 = 15.04116466 0.25 + -0.4016064257x + x2 = 15.04116466 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 15.04116466 Calculate the square root of the right side: 3.87829404 Break this problem into two subproblems by setting (x + 0.5) equal to 3.87829404 and -3.87829404.Subproblem 1
x + 0.5 = 3.87829404 Simplifying x + 0.5 = 3.87829404 Reorder the terms: 0.5 + x = 3.87829404 Solving 0.5 + x = 3.87829404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 3.87829404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.87829404 + -0.5 x = 3.87829404 + -0.5 Combine like terms: 3.87829404 + -0.5 = 3.37829404 x = 3.37829404 Simplifying x = 3.37829404Subproblem 2
x + 0.5 = -3.87829404 Simplifying x + 0.5 = -3.87829404 Reorder the terms: 0.5 + x = -3.87829404 Solving 0.5 + x = -3.87829404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -3.87829404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.87829404 + -0.5 x = -3.87829404 + -0.5 Combine like terms: -3.87829404 + -0.5 = -4.37829404 x = -4.37829404 Simplifying x = -4.37829404Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.37829404, -4.37829404}
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