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Simplifying 25x2 + -30x + 9 + -11 + -4x + -1 = 1 Reorder the terms: 9 + -11 + -1 + -30x + -4x + 25x2 = 1 Combine like terms: 9 + -11 = -2 -2 + -1 + -30x + -4x + 25x2 = 1 Combine like terms: -2 + -1 = -3 -3 + -30x + -4x + 25x2 = 1 Combine like terms: -30x + -4x = -34x -3 + -34x + 25x2 = 1 Solving -3 + -34x + 25x2 = 1 Solving for variable 'x'. Reorder the terms: -3 + -1 + -34x + 25x2 = 1 + -1 Combine like terms: -3 + -1 = -4 -4 + -34x + 25x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -4 + -34x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.16 + -1.36x + x2 = 0 Move the constant term to the right: Add '0.16' to each side of the equation. -0.16 + -1.36x + 0.16 + x2 = 0 + 0.16 Reorder the terms: -0.16 + 0.16 + -1.36x + x2 = 0 + 0.16 Combine like terms: -0.16 + 0.16 = 0.00 0.00 + -1.36x + x2 = 0 + 0.16 -1.36x + x2 = 0 + 0.16 Combine like terms: 0 + 0.16 = 0.16 -1.36x + x2 = 0.16 The x term is -1.36x. Take half its coefficient (-0.68). Square it (0.4624) and add it to both sides. Add '0.4624' to each side of the equation. -1.36x + 0.4624 + x2 = 0.16 + 0.4624 Reorder the terms: 0.4624 + -1.36x + x2 = 0.16 + 0.4624 Combine like terms: 0.16 + 0.4624 = 0.6224 0.4624 + -1.36x + x2 = 0.6224 Factor a perfect square on the left side: (x + -0.68)(x + -0.68) = 0.6224 Calculate the square root of the right side: 0.788923317 Break this problem into two subproblems by setting (x + -0.68) equal to 0.788923317 and -0.788923317.Subproblem 1
x + -0.68 = 0.788923317 Simplifying x + -0.68 = 0.788923317 Reorder the terms: -0.68 + x = 0.788923317 Solving -0.68 + x = 0.788923317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.68' to each side of the equation. -0.68 + 0.68 + x = 0.788923317 + 0.68 Combine like terms: -0.68 + 0.68 = 0.00 0.00 + x = 0.788923317 + 0.68 x = 0.788923317 + 0.68 Combine like terms: 0.788923317 + 0.68 = 1.468923317 x = 1.468923317 Simplifying x = 1.468923317Subproblem 2
x + -0.68 = -0.788923317 Simplifying x + -0.68 = -0.788923317 Reorder the terms: -0.68 + x = -0.788923317 Solving -0.68 + x = -0.788923317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.68' to each side of the equation. -0.68 + 0.68 + x = -0.788923317 + 0.68 Combine like terms: -0.68 + 0.68 = 0.00 0.00 + x = -0.788923317 + 0.68 x = -0.788923317 + 0.68 Combine like terms: -0.788923317 + 0.68 = -0.108923317 x = -0.108923317 Simplifying x = -0.108923317Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.468923317, -0.108923317}
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