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Simplifying (x + -3)(x + -3) + 2x + 9 = 9 * 9 + 3x + 2 Reorder the terms: (-3 + x)(x + -3) + 2x + 9 = 9 * 9 + 3x + 2 Reorder the terms: (-3 + x)(-3 + x) + 2x + 9 = 9 * 9 + 3x + 2 Multiply (-3 + x) * (-3 + x) (-3(-3 + x) + x(-3 + x)) + 2x + 9 = 9 * 9 + 3x + 2 ((-3 * -3 + x * -3) + x(-3 + x)) + 2x + 9 = 9 * 9 + 3x + 2 ((9 + -3x) + x(-3 + x)) + 2x + 9 = 9 * 9 + 3x + 2 (9 + -3x + (-3 * x + x * x)) + 2x + 9 = 9 * 9 + 3x + 2 (9 + -3x + (-3x + x2)) + 2x + 9 = 9 * 9 + 3x + 2 Combine like terms: -3x + -3x = -6x (9 + -6x + x2) + 2x + 9 = 9 * 9 + 3x + 2 Reorder the terms: 9 + 9 + -6x + 2x + x2 = 9 * 9 + 3x + 2 Combine like terms: 9 + 9 = 18 18 + -6x + 2x + x2 = 9 * 9 + 3x + 2 Combine like terms: -6x + 2x = -4x 18 + -4x + x2 = 9 * 9 + 3x + 2 Multiply 9 * 9 18 + -4x + x2 = 81 + 3x + 2 Reorder the terms: 18 + -4x + x2 = 81 + 2 + 3x Combine like terms: 81 + 2 = 83 18 + -4x + x2 = 83 + 3x Solving 18 + -4x + x2 = 83 + 3x Solving for variable 'x'. Reorder the terms: 18 + -83 + -4x + -3x + x2 = 83 + 3x + -83 + -3x Combine like terms: 18 + -83 = -65 -65 + -4x + -3x + x2 = 83 + 3x + -83 + -3x Combine like terms: -4x + -3x = -7x -65 + -7x + x2 = 83 + 3x + -83 + -3x Reorder the terms: -65 + -7x + x2 = 83 + -83 + 3x + -3x Combine like terms: 83 + -83 = 0 -65 + -7x + x2 = 0 + 3x + -3x -65 + -7x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -65 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '65' to each side of the equation. -65 + -7x + 65 + x2 = 0 + 65 Reorder the terms: -65 + 65 + -7x + x2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + -7x + x2 = 0 + 65 -7x + x2 = 0 + 65 Combine like terms: 0 + 65 = 65 -7x + x2 = 65 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 65 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 65 + 12.25 Combine like terms: 65 + 12.25 = 77.25 12.25 + -7x + x2 = 77.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 77.25 Calculate the square root of the right side: 8.789197916 Break this problem into two subproblems by setting (x + -3.5) equal to 8.789197916 and -8.789197916.Subproblem 1
x + -3.5 = 8.789197916 Simplifying x + -3.5 = 8.789197916 Reorder the terms: -3.5 + x = 8.789197916 Solving -3.5 + x = 8.789197916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 8.789197916 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 8.789197916 + 3.5 x = 8.789197916 + 3.5 Combine like terms: 8.789197916 + 3.5 = 12.289197916 x = 12.289197916 Simplifying x = 12.289197916Subproblem 2
x + -3.5 = -8.789197916 Simplifying x + -3.5 = -8.789197916 Reorder the terms: -3.5 + x = -8.789197916 Solving -3.5 + x = -8.789197916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -8.789197916 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -8.789197916 + 3.5 x = -8.789197916 + 3.5 Combine like terms: -8.789197916 + 3.5 = -5.289197916 x = -5.289197916 Simplifying x = -5.289197916Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.289197916, -5.289197916}
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