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Simplifying (x + -4)(4x + 1) = x(3 + 1) Reorder the terms: (-4 + x)(4x + 1) = x(3 + 1) Reorder the terms: (-4 + x)(1 + 4x) = x(3 + 1) Multiply (-4 + x) * (1 + 4x) (-4(1 + 4x) + x(1 + 4x)) = x(3 + 1) ((1 * -4 + 4x * -4) + x(1 + 4x)) = x(3 + 1) ((-4 + -16x) + x(1 + 4x)) = x(3 + 1) (-4 + -16x + (1 * x + 4x * x)) = x(3 + 1) (-4 + -16x + (1x + 4x2)) = x(3 + 1) Combine like terms: -16x + 1x = -15x (-4 + -15x + 4x2) = x(3 + 1) Combine like terms: 3 + 1 = 4 -4 + -15x + 4x2 = x(4) Reorder the terms for easier multiplication: -4 + -15x + 4x2 = 4x Solving -4 + -15x + 4x2 = 4x Solving for variable 'x'. Reorder the terms: -4 + -15x + -4x + 4x2 = 4x + -4x Combine like terms: -15x + -4x = -19x -4 + -19x + 4x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -4 + -19x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + -4.75x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -4.75x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -4.75x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4.75x + x2 = 0 + 1 -4.75x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -4.75x + x2 = 1 The x term is -4.75x. Take half its coefficient (-2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. -4.75x + 5.640625 + x2 = 1 + 5.640625 Reorder the terms: 5.640625 + -4.75x + x2 = 1 + 5.640625 Combine like terms: 1 + 5.640625 = 6.640625 5.640625 + -4.75x + x2 = 6.640625 Factor a perfect square on the left side: (x + -2.375)(x + -2.375) = 6.640625 Calculate the square root of the right side: 2.576941016 Break this problem into two subproblems by setting (x + -2.375) equal to 2.576941016 and -2.576941016.Subproblem 1
x + -2.375 = 2.576941016 Simplifying x + -2.375 = 2.576941016 Reorder the terms: -2.375 + x = 2.576941016 Solving -2.375 + x = 2.576941016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = 2.576941016 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 2.576941016 + 2.375 x = 2.576941016 + 2.375 Combine like terms: 2.576941016 + 2.375 = 4.951941016 x = 4.951941016 Simplifying x = 4.951941016Subproblem 2
x + -2.375 = -2.576941016 Simplifying x + -2.375 = -2.576941016 Reorder the terms: -2.375 + x = -2.576941016 Solving -2.375 + x = -2.576941016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = -2.576941016 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -2.576941016 + 2.375 x = -2.576941016 + 2.375 Combine like terms: -2.576941016 + 2.375 = -0.201941016 x = -0.201941016 Simplifying x = -0.201941016Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.951941016, -0.201941016}
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