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Simplifying (x + -3)(x + 6) = 3 Reorder the terms: (-3 + x)(x + 6) = 3 Reorder the terms: (-3 + x)(6 + x) = 3 Multiply (-3 + x) * (6 + x) (-3(6 + x) + x(6 + x)) = 3 ((6 * -3 + x * -3) + x(6 + x)) = 3 ((-18 + -3x) + x(6 + x)) = 3 (-18 + -3x + (6 * x + x * x)) = 3 (-18 + -3x + (6x + x2)) = 3 Combine like terms: -3x + 6x = 3x (-18 + 3x + x2) = 3 Solving -18 + 3x + x2 = 3 Solving for variable 'x'. Reorder the terms: -18 + -3 + 3x + x2 = 3 + -3 Combine like terms: -18 + -3 = -21 -21 + 3x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -21 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 3x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 3x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 3x + x2 = 0 + 21 3x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 3x + x2 = 21 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 = 21 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 21 + 2.25 Combine like terms: 21 + 2.25 = 23.25 2.25 + 3x + x2 = 23.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting (x + 1.5) equal to 4.82182538 and -4.82182538.Subproblem 1
x + 1.5 = 4.82182538 Simplifying x + 1.5 = 4.82182538 Reorder the terms: 1.5 + x = 4.82182538 Solving 1.5 + x = 4.82182538 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 = 4.82182538 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 4.82182538 + -1.5 x = 4.82182538 + -1.5 Combine like terms: 4.82182538 + -1.5 = 3.32182538 x = 3.32182538 Simplifying x = 3.32182538Subproblem 2
x + 1.5 = -4.82182538 Simplifying x + 1.5 = -4.82182538 Reorder the terms: 1.5 + x = -4.82182538 Solving 1.5 + x = -4.82182538 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 = -4.82182538 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -4.82182538 + -1.5 x = -4.82182538 + -1.5 Combine like terms: -4.82182538 + -1.5 = -6.32182538 x = -6.32182538 Simplifying x = -6.32182538Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.32182538, -6.32182538}
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