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Simplifying (7x + 8)(x + -5) = x Reorder the terms: (8 + 7x)(x + -5) = x Reorder the terms: (8 + 7x)(-5 + x) = x Multiply (8 + 7x) * (-5 + x) (8(-5 + x) + 7x * (-5 + x)) = x ((-5 * 8 + x * 8) + 7x * (-5 + x)) = x ((-40 + 8x) + 7x * (-5 + x)) = x (-40 + 8x + (-5 * 7x + x * 7x)) = x (-40 + 8x + (-35x + 7x2)) = x Combine like terms: 8x + -35x = -27x (-40 + -27x + 7x2) = x Solving -40 + -27x + 7x2 = x Solving for variable 'x'. Reorder the terms: -40 + -27x + -1x + 7x2 = x + -1x Combine like terms: -27x + -1x = -28x -40 + -28x + 7x2 = x + -1x Combine like terms: x + -1x = 0 -40 + -28x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5.714285714 + -4x + x2 = 0 Move the constant term to the right: Add '5.714285714' to each side of the equation. -5.714285714 + -4x + 5.714285714 + x2 = 0 + 5.714285714 Reorder the terms: -5.714285714 + 5.714285714 + -4x + x2 = 0 + 5.714285714 Combine like terms: -5.714285714 + 5.714285714 = 0.000000000 0.000000000 + -4x + x2 = 0 + 5.714285714 -4x + x2 = 0 + 5.714285714 Combine like terms: 0 + 5.714285714 = 5.714285714 -4x + x2 = 5.714285714 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 5.714285714 + 4 Reorder the terms: 4 + -4x + x2 = 5.714285714 + 4 Combine like terms: 5.714285714 + 4 = 9.714285714 4 + -4x + x2 = 9.714285714 Factor a perfect square on the left side: (x + -2)(x + -2) = 9.714285714 Calculate the square root of the right side: 3.11677489 Break this problem into two subproblems by setting (x + -2) equal to 3.11677489 and -3.11677489.Subproblem 1
x + -2 = 3.11677489 Simplifying x + -2 = 3.11677489 Reorder the terms: -2 + x = 3.11677489 Solving -2 + x = 3.11677489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.11677489 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.11677489 + 2 x = 3.11677489 + 2 Combine like terms: 3.11677489 + 2 = 5.11677489 x = 5.11677489 Simplifying x = 5.11677489Subproblem 2
x + -2 = -3.11677489 Simplifying x + -2 = -3.11677489 Reorder the terms: -2 + x = -3.11677489 Solving -2 + x = -3.11677489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.11677489 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.11677489 + 2 x = -3.11677489 + 2 Combine like terms: -3.11677489 + 2 = -1.11677489 x = -1.11677489 Simplifying x = -1.11677489Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.11677489, -1.11677489}
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