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Simplifying (2x + -6)(x + 7) = x Reorder the terms: (-6 + 2x)(x + 7) = x Reorder the terms: (-6 + 2x)(7 + x) = x Multiply (-6 + 2x) * (7 + x) (-6(7 + x) + 2x * (7 + x)) = x ((7 * -6 + x * -6) + 2x * (7 + x)) = x ((-42 + -6x) + 2x * (7 + x)) = x (-42 + -6x + (7 * 2x + x * 2x)) = x (-42 + -6x + (14x + 2x2)) = x Combine like terms: -6x + 14x = 8x (-42 + 8x + 2x2) = x Solving -42 + 8x + 2x2 = x Solving for variable 'x'. Reorder the terms: -42 + 8x + -1x + 2x2 = x + -1x Combine like terms: 8x + -1x = 7x -42 + 7x + 2x2 = x + -1x Combine like terms: x + -1x = 0 -42 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -21 + 3.5x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + 3.5x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 3.5x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 3.5x + x2 = 0 + 21 3.5x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 3.5x + x2 = 21 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 21 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 21 + 3.0625 Combine like terms: 21 + 3.0625 = 24.0625 3.0625 + 3.5x + x2 = 24.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 24.0625 Calculate the square root of the right side: 4.905354218 Break this problem into two subproblems by setting (x + 1.75) equal to 4.905354218 and -4.905354218.Subproblem 1
x + 1.75 = 4.905354218 Simplifying x + 1.75 = 4.905354218 Reorder the terms: 1.75 + x = 4.905354218 Solving 1.75 + x = 4.905354218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 4.905354218 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 4.905354218 + -1.75 x = 4.905354218 + -1.75 Combine like terms: 4.905354218 + -1.75 = 3.155354218 x = 3.155354218 Simplifying x = 3.155354218Subproblem 2
x + 1.75 = -4.905354218 Simplifying x + 1.75 = -4.905354218 Reorder the terms: 1.75 + x = -4.905354218 Solving 1.75 + x = -4.905354218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -4.905354218 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -4.905354218 + -1.75 x = -4.905354218 + -1.75 Combine like terms: -4.905354218 + -1.75 = -6.655354218 x = -6.655354218 Simplifying x = -6.655354218Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.155354218, -6.655354218}
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