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Simplifying x(x + -1) + -1(x + -1) + 3 = 9 Reorder the terms: x(-1 + x) + -1(x + -1) + 3 = 9 (-1 * x + x * x) + -1(x + -1) + 3 = 9 (-1x + x2) + -1(x + -1) + 3 = 9 Reorder the terms: -1x + x2 + -1(-1 + x) + 3 = 9 -1x + x2 + (-1 * -1 + x * -1) + 3 = 9 -1x + x2 + (1 + -1x) + 3 = 9 Reorder the terms: 1 + 3 + -1x + -1x + x2 = 9 Combine like terms: 1 + 3 = 4 4 + -1x + -1x + x2 = 9 Combine like terms: -1x + -1x = -2x 4 + -2x + x2 = 9 Solving 4 + -2x + x2 = 9 Solving for variable 'x'. Reorder the terms: 4 + -9 + -2x + x2 = 9 + -9 Combine like terms: 4 + -9 = -5 -5 + -2x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -5 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -2x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -2x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x + x2 = 0 + 5 -2x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2x + x2 = 5 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 = 5 + 1 Reorder the terms: 1 + -2x + x2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + -2x + x2 = 6 Factor a perfect square on the left side: (x + -1)(x + -1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -1) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -1 = 2.449489743 Simplifying x + -1 = 2.449489743 Reorder the terms: -1 + x = 2.449489743 Solving -1 + x = 2.449489743 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 = 2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.449489743 + 1 x = 2.449489743 + 1 Combine like terms: 2.449489743 + 1 = 3.449489743 x = 3.449489743 Simplifying x = 3.449489743Subproblem 2
x + -1 = -2.449489743 Simplifying x + -1 = -2.449489743 Reorder the terms: -1 + x = -2.449489743 Solving -1 + x = -2.449489743 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 = -2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.449489743 + 1 x = -2.449489743 + 1 Combine like terms: -2.449489743 + 1 = -1.449489743 x = -1.449489743 Simplifying x = -1.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.449489743, -1.449489743}
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