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Simplifying 175 = (4x + -1)(x + 1) Reorder the terms: 175 = (-1 + 4x)(x + 1) Reorder the terms: 175 = (-1 + 4x)(1 + x) Multiply (-1 + 4x) * (1 + x) 175 = (-1(1 + x) + 4x * (1 + x)) 175 = ((1 * -1 + x * -1) + 4x * (1 + x)) 175 = ((-1 + -1x) + 4x * (1 + x)) 175 = (-1 + -1x + (1 * 4x + x * 4x)) 175 = (-1 + -1x + (4x + 4x2)) Combine like terms: -1x + 4x = 3x 175 = (-1 + 3x + 4x2) Solving 175 = -1 + 3x + 4x2 Solving for variable 'x'. Combine like terms: 175 + 1 = 176 176 + -3x + -4x2 = -1 + 3x + 4x2 + 1 + -3x + -4x2 Reorder the terms: 176 + -3x + -4x2 = -1 + 1 + 3x + -3x + 4x2 + -4x2 Combine like terms: -1 + 1 = 0 176 + -3x + -4x2 = 0 + 3x + -3x + 4x2 + -4x2 176 + -3x + -4x2 = 3x + -3x + 4x2 + -4x2 Combine like terms: 3x + -3x = 0 176 + -3x + -4x2 = 0 + 4x2 + -4x2 176 + -3x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 176 + -3x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -44 + 0.75x + x2 = 0 Move the constant term to the right: Add '44' to each side of the equation. -44 + 0.75x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + 0.75x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 0.75x + x2 = 0 + 44 0.75x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 0.75x + x2 = 44 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 = 44 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 44 + 0.140625 Combine like terms: 44 + 0.140625 = 44.140625 0.140625 + 0.75x + x2 = 44.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 44.140625 Calculate the square root of the right side: 6.643841133 Break this problem into two subproblems by setting (x + 0.375) equal to 6.643841133 and -6.643841133.Subproblem 1
x + 0.375 = 6.643841133 Simplifying x + 0.375 = 6.643841133 Reorder the terms: 0.375 + x = 6.643841133 Solving 0.375 + x = 6.643841133 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 = 6.643841133 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 6.643841133 + -0.375 x = 6.643841133 + -0.375 Combine like terms: 6.643841133 + -0.375 = 6.268841133 x = 6.268841133 Simplifying x = 6.268841133Subproblem 2
x + 0.375 = -6.643841133 Simplifying x + 0.375 = -6.643841133 Reorder the terms: 0.375 + x = -6.643841133 Solving 0.375 + x = -6.643841133 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 = -6.643841133 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -6.643841133 + -0.375 x = -6.643841133 + -0.375 Combine like terms: -6.643841133 + -0.375 = -7.018841133 x = -7.018841133 Simplifying x = -7.018841133Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.268841133, -7.018841133}
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