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Simplifying 4x2 + -1 = 3x + 25 Reorder the terms: -1 + 4x2 = 3x + 25 Reorder the terms: -1 + 4x2 = 25 + 3x Solving -1 + 4x2 = 25 + 3x Solving for variable 'x'. Reorder the terms: -1 + -25 + -3x + 4x2 = 25 + 3x + -25 + -3x Combine like terms: -1 + -25 = -26 -26 + -3x + 4x2 = 25 + 3x + -25 + -3x Reorder the terms: -26 + -3x + 4x2 = 25 + -25 + 3x + -3x Combine like terms: 25 + -25 = 0 -26 + -3x + 4x2 = 0 + 3x + -3x -26 + -3x + 4x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -26 + -3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.5 + -0.75x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + -0.75x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + -0.75x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + -0.75x + x2 = 0 + 6.5 -0.75x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 -0.75x + x2 = 6.5 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 6.5 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 6.5 + 0.140625 Combine like terms: 6.5 + 0.140625 = 6.640625 0.140625 + -0.75x + x2 = 6.640625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 6.640625 Calculate the square root of the right side: 2.576941016 Break this problem into two subproblems by setting (x + -0.375) equal to 2.576941016 and -2.576941016.Subproblem 1
x + -0.375 = 2.576941016 Simplifying x + -0.375 = 2.576941016 Reorder the terms: -0.375 + x = 2.576941016 Solving -0.375 + x = 2.576941016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 2.576941016 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 2.576941016 + 0.375 x = 2.576941016 + 0.375 Combine like terms: 2.576941016 + 0.375 = 2.951941016 x = 2.951941016 Simplifying x = 2.951941016Subproblem 2
x + -0.375 = -2.576941016 Simplifying x + -0.375 = -2.576941016 Reorder the terms: -0.375 + x = -2.576941016 Solving -0.375 + x = -2.576941016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -2.576941016 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -2.576941016 + 0.375 x = -2.576941016 + 0.375 Combine like terms: -2.576941016 + 0.375 = -2.201941016 x = -2.201941016 Simplifying x = -2.201941016Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.951941016, -2.201941016}
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