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Simplifying -7x = (4x + 9)(x + -1) Reorder the terms: -7x = (9 + 4x)(x + -1) Reorder the terms: -7x = (9 + 4x)(-1 + x) Multiply (9 + 4x) * (-1 + x) -7x = (9(-1 + x) + 4x * (-1 + x)) -7x = ((-1 * 9 + x * 9) + 4x * (-1 + x)) -7x = ((-9 + 9x) + 4x * (-1 + x)) -7x = (-9 + 9x + (-1 * 4x + x * 4x)) -7x = (-9 + 9x + (-4x + 4x2)) Combine like terms: 9x + -4x = 5x -7x = (-9 + 5x + 4x2) Solving -7x = -9 + 5x + 4x2 Solving for variable 'x'. Reorder the terms: 9 + -7x + -5x + -4x2 = -9 + 5x + 4x2 + 9 + -5x + -4x2 Combine like terms: -7x + -5x = -12x 9 + -12x + -4x2 = -9 + 5x + 4x2 + 9 + -5x + -4x2 Reorder the terms: 9 + -12x + -4x2 = -9 + 9 + 5x + -5x + 4x2 + -4x2 Combine like terms: -9 + 9 = 0 9 + -12x + -4x2 = 0 + 5x + -5x + 4x2 + -4x2 9 + -12x + -4x2 = 5x + -5x + 4x2 + -4x2 Combine like terms: 5x + -5x = 0 9 + -12x + -4x2 = 0 + 4x2 + -4x2 9 + -12x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 9 + -12x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.25 + 3x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 3x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 3x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 3x + x2 = 0 + 2.25 3x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 3x + x2 = 2.25 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 2.25 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 2.25 + 2.25 Combine like terms: 2.25 + 2.25 = 4.5 2.25 + 3x + x2 = 4.5 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (x + 1.5) equal to 2.121320344 and -2.121320344.Subproblem 1
x + 1.5 = 2.121320344 Simplifying x + 1.5 = 2.121320344 Reorder the terms: 1.5 + x = 2.121320344 Solving 1.5 + x = 2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.121320344 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.121320344 + -1.5 x = 2.121320344 + -1.5 Combine like terms: 2.121320344 + -1.5 = 0.621320344 x = 0.621320344 Simplifying x = 0.621320344Subproblem 2
x + 1.5 = -2.121320344 Simplifying x + 1.5 = -2.121320344 Reorder the terms: 1.5 + x = -2.121320344 Solving 1.5 + x = -2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.121320344 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.121320344 + -1.5 x = -2.121320344 + -1.5 Combine like terms: -2.121320344 + -1.5 = -3.621320344 x = -3.621320344 Simplifying x = -3.621320344Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.621320344, -3.621320344}
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