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Simplifying 7x + -9 = (x + 1)(x + -3) Reorder the terms: -9 + 7x = (x + 1)(x + -3) Reorder the terms: -9 + 7x = (1 + x)(x + -3) Reorder the terms: -9 + 7x = (1 + x)(-3 + x) Multiply (1 + x) * (-3 + x) -9 + 7x = (1(-3 + x) + x(-3 + x)) -9 + 7x = ((-3 * 1 + x * 1) + x(-3 + x)) -9 + 7x = ((-3 + 1x) + x(-3 + x)) -9 + 7x = (-3 + 1x + (-3 * x + x * x)) -9 + 7x = (-3 + 1x + (-3x + x2)) Combine like terms: 1x + -3x = -2x -9 + 7x = (-3 + -2x + x2) Solving -9 + 7x = -3 + -2x + x2 Solving for variable 'x'. Reorder the terms: -9 + 3 + 7x + 2x + -1x2 = -3 + -2x + x2 + 3 + 2x + -1x2 Combine like terms: -9 + 3 = -6 -6 + 7x + 2x + -1x2 = -3 + -2x + x2 + 3 + 2x + -1x2 Combine like terms: 7x + 2x = 9x -6 + 9x + -1x2 = -3 + -2x + x2 + 3 + 2x + -1x2 Reorder the terms: -6 + 9x + -1x2 = -3 + 3 + -2x + 2x + x2 + -1x2 Combine like terms: -3 + 3 = 0 -6 + 9x + -1x2 = 0 + -2x + 2x + x2 + -1x2 -6 + 9x + -1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 -6 + 9x + -1x2 = 0 + x2 + -1x2 -6 + 9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -6 + 9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 6 + -9x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -9x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -9x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -9x + x2 = 0 + -6 -9x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -9x + x2 = -6 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -6 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -6 + 20.25 Combine like terms: -6 + 20.25 = 14.25 20.25 + -9x + x2 = 14.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x + -4.5) equal to 3.774917218 and -3.774917218.Subproblem 1
x + -4.5 = 3.774917218 Simplifying x + -4.5 = 3.774917218 Reorder the terms: -4.5 + x = 3.774917218 Solving -4.5 + x = 3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 3.774917218 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 3.774917218 + 4.5 x = 3.774917218 + 4.5 Combine like terms: 3.774917218 + 4.5 = 8.274917218 x = 8.274917218 Simplifying x = 8.274917218Subproblem 2
x + -4.5 = -3.774917218 Simplifying x + -4.5 = -3.774917218 Reorder the terms: -4.5 + x = -3.774917218 Solving -4.5 + x = -3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -3.774917218 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -3.774917218 + 4.5 x = -3.774917218 + 4.5 Combine like terms: -3.774917218 + 4.5 = 0.725082782 x = 0.725082782 Simplifying x = 0.725082782Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.274917218, 0.725082782}
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