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Simplifying (4x + -1)(2x + 5) = 7x Reorder the terms: (-1 + 4x)(2x + 5) = 7x Reorder the terms: (-1 + 4x)(5 + 2x) = 7x Multiply (-1 + 4x) * (5 + 2x) (-1(5 + 2x) + 4x * (5 + 2x)) = 7x ((5 * -1 + 2x * -1) + 4x * (5 + 2x)) = 7x ((-5 + -2x) + 4x * (5 + 2x)) = 7x (-5 + -2x + (5 * 4x + 2x * 4x)) = 7x (-5 + -2x + (20x + 8x2)) = 7x Combine like terms: -2x + 20x = 18x (-5 + 18x + 8x2) = 7x Solving -5 + 18x + 8x2 = 7x Solving for variable 'x'. Reorder the terms: -5 + 18x + -7x + 8x2 = 7x + -7x Combine like terms: 18x + -7x = 11x -5 + 11x + 8x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -5 + 11x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + 1.375x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 1.375x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 1.375x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 1.375x + x2 = 0 + 0.625 1.375x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 1.375x + x2 = 0.625 The x term is 1.375x. Take half its coefficient (0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. 1.375x + 0.47265625 + x2 = 0.625 + 0.47265625 Reorder the terms: 0.47265625 + 1.375x + x2 = 0.625 + 0.47265625 Combine like terms: 0.625 + 0.47265625 = 1.09765625 0.47265625 + 1.375x + x2 = 1.09765625 Factor a perfect square on the left side: (x + 0.6875)(x + 0.6875) = 1.09765625 Calculate the square root of the right side: 1.047690913 Break this problem into two subproblems by setting (x + 0.6875) equal to 1.047690913 and -1.047690913.Subproblem 1
x + 0.6875 = 1.047690913 Simplifying x + 0.6875 = 1.047690913 Reorder the terms: 0.6875 + x = 1.047690913 Solving 0.6875 + x = 1.047690913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + x = 1.047690913 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = 1.047690913 + -0.6875 x = 1.047690913 + -0.6875 Combine like terms: 1.047690913 + -0.6875 = 0.360190913 x = 0.360190913 Simplifying x = 0.360190913Subproblem 2
x + 0.6875 = -1.047690913 Simplifying x + 0.6875 = -1.047690913 Reorder the terms: 0.6875 + x = -1.047690913 Solving 0.6875 + x = -1.047690913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + x = -1.047690913 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = -1.047690913 + -0.6875 x = -1.047690913 + -0.6875 Combine like terms: -1.047690913 + -0.6875 = -1.735190913 x = -1.735190913 Simplifying x = -1.735190913Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.360190913, -1.735190913}
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