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Simplifying x(x + 1) = 3(x + 6) Reorder the terms: x(1 + x) = 3(x + 6) (1 * x + x * x) = 3(x + 6) (1x + x2) = 3(x + 6) Reorder the terms: 1x + x2 = 3(6 + x) 1x + x2 = (6 * 3 + x * 3) 1x + x2 = (18 + 3x) Solving 1x + x2 = 18 + 3x Solving for variable 'x'. Reorder the terms: -18 + 1x + -3x + x2 = 18 + 3x + -18 + -3x Combine like terms: 1x + -3x = -2x -18 + -2x + x2 = 18 + 3x + -18 + -3x Reorder the terms: -18 + -2x + x2 = 18 + -18 + 3x + -3x Combine like terms: 18 + -18 = 0 -18 + -2x + x2 = 0 + 3x + -3x -18 + -2x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -18 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -2x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -2x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -2x + x2 = 0 + 18 -2x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -2x + x2 = 18 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 = 18 + 1 Reorder the terms: 1 + -2x + x2 = 18 + 1 Combine like terms: 18 + 1 = 19 1 + -2x + x2 = 19 Factor a perfect square on the left side: (x + -1)(x + -1) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + -1) equal to 4.358898944 and -4.358898944.Subproblem 1
x + -1 = 4.358898944 Simplifying x + -1 = 4.358898944 Reorder the terms: -1 + x = 4.358898944 Solving -1 + x = 4.358898944 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 = 4.358898944 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.358898944 + 1 x = 4.358898944 + 1 Combine like terms: 4.358898944 + 1 = 5.358898944 x = 5.358898944 Simplifying x = 5.358898944Subproblem 2
x + -1 = -4.358898944 Simplifying x + -1 = -4.358898944 Reorder the terms: -1 + x = -4.358898944 Solving -1 + x = -4.358898944 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 = -4.358898944 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.358898944 + 1 x = -4.358898944 + 1 Combine like terms: -4.358898944 + 1 = -3.358898944 x = -3.358898944 Simplifying x = -3.358898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.358898944, -3.358898944}
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