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Simplifying (5x + 2)(x + -1) = 7x Reorder the terms: (2 + 5x)(x + -1) = 7x Reorder the terms: (2 + 5x)(-1 + x) = 7x Multiply (2 + 5x) * (-1 + x) (2(-1 + x) + 5x * (-1 + x)) = 7x ((-1 * 2 + x * 2) + 5x * (-1 + x)) = 7x ((-2 + 2x) + 5x * (-1 + x)) = 7x (-2 + 2x + (-1 * 5x + x * 5x)) = 7x (-2 + 2x + (-5x + 5x2)) = 7x Combine like terms: 2x + -5x = -3x (-2 + -3x + 5x2) = 7x Solving -2 + -3x + 5x2 = 7x Solving for variable 'x'. Reorder the terms: -2 + -3x + -7x + 5x2 = 7x + -7x Combine like terms: -3x + -7x = -10x -2 + -10x + 5x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -2 + -10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -2x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -2x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -2x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -2x + x2 = 0 + 0.4 -2x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -2x + x2 = 0.4 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 0.4 + 1 Reorder the terms: 1 + -2x + x2 = 0.4 + 1 Combine like terms: 0.4 + 1 = 1.4 1 + -2x + x2 = 1.4 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.4 Calculate the square root of the right side: 1.183215957 Break this problem into two subproblems by setting (x + -1) equal to 1.183215957 and -1.183215957.Subproblem 1
x + -1 = 1.183215957 Simplifying x + -1 = 1.183215957 Reorder the terms: -1 + x = 1.183215957 Solving -1 + x = 1.183215957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.183215957 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.183215957 + 1 x = 1.183215957 + 1 Combine like terms: 1.183215957 + 1 = 2.183215957 x = 2.183215957 Simplifying x = 2.183215957Subproblem 2
x + -1 = -1.183215957 Simplifying x + -1 = -1.183215957 Reorder the terms: -1 + x = -1.183215957 Solving -1 + x = -1.183215957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.183215957 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.183215957 + 1 x = -1.183215957 + 1 Combine like terms: -1.183215957 + 1 = -0.183215957 x = -0.183215957 Simplifying x = -0.183215957Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.183215957, -0.183215957}
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