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Simplifying 4x(x + -7) = 7(x + -5) Reorder the terms: 4x(-7 + x) = 7(x + -5) (-7 * 4x + x * 4x) = 7(x + -5) (-28x + 4x2) = 7(x + -5) Reorder the terms: -28x + 4x2 = 7(-5 + x) -28x + 4x2 = (-5 * 7 + x * 7) -28x + 4x2 = (-35 + 7x) Solving -28x + 4x2 = -35 + 7x Solving for variable 'x'. Reorder the terms: 35 + -28x + -7x + 4x2 = -35 + 7x + 35 + -7x Combine like terms: -28x + -7x = -35x 35 + -35x + 4x2 = -35 + 7x + 35 + -7x Reorder the terms: 35 + -35x + 4x2 = -35 + 35 + 7x + -7x Combine like terms: -35 + 35 = 0 35 + -35x + 4x2 = 0 + 7x + -7x 35 + -35x + 4x2 = 7x + -7x Combine like terms: 7x + -7x = 0 35 + -35x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 8.75 + -8.75x + x2 = 0 Move the constant term to the right: Add '-8.75' to each side of the equation. 8.75 + -8.75x + -8.75 + x2 = 0 + -8.75 Reorder the terms: 8.75 + -8.75 + -8.75x + x2 = 0 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + -8.75x + x2 = 0 + -8.75 -8.75x + x2 = 0 + -8.75 Combine like terms: 0 + -8.75 = -8.75 -8.75x + x2 = -8.75 The x term is -8.75x. Take half its coefficient (-4.375). Square it (19.140625) and add it to both sides. Add '19.140625' to each side of the equation. -8.75x + 19.140625 + x2 = -8.75 + 19.140625 Reorder the terms: 19.140625 + -8.75x + x2 = -8.75 + 19.140625 Combine like terms: -8.75 + 19.140625 = 10.390625 19.140625 + -8.75x + x2 = 10.390625 Factor a perfect square on the left side: (x + -4.375)(x + -4.375) = 10.390625 Calculate the square root of the right side: 3.22344924 Break this problem into two subproblems by setting (x + -4.375) equal to 3.22344924 and -3.22344924.Subproblem 1
x + -4.375 = 3.22344924 Simplifying x + -4.375 = 3.22344924 Reorder the terms: -4.375 + x = 3.22344924 Solving -4.375 + x = 3.22344924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = 3.22344924 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = 3.22344924 + 4.375 x = 3.22344924 + 4.375 Combine like terms: 3.22344924 + 4.375 = 7.59844924 x = 7.59844924 Simplifying x = 7.59844924Subproblem 2
x + -4.375 = -3.22344924 Simplifying x + -4.375 = -3.22344924 Reorder the terms: -4.375 + x = -3.22344924 Solving -4.375 + x = -3.22344924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = -3.22344924 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = -3.22344924 + 4.375 x = -3.22344924 + 4.375 Combine like terms: -3.22344924 + 4.375 = 1.15155076 x = 1.15155076 Simplifying x = 1.15155076Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.59844924, 1.15155076}
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