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Simplifying (x + 3)(x + 3) + 24x = 0 Reorder the terms: (3 + x)(x + 3) + 24x = 0 Reorder the terms: (3 + x)(3 + x) + 24x = 0 Multiply (3 + x) * (3 + x) (3(3 + x) + x(3 + x)) + 24x = 0 ((3 * 3 + x * 3) + x(3 + x)) + 24x = 0 ((9 + 3x) + x(3 + x)) + 24x = 0 (9 + 3x + (3 * x + x * x)) + 24x = 0 (9 + 3x + (3x + x2)) + 24x = 0 Combine like terms: 3x + 3x = 6x (9 + 6x + x2) + 24x = 0 Reorder the terms: 9 + 6x + 24x + x2 = 0 Combine like terms: 6x + 24x = 30x 9 + 30x + x2 = 0 Solving 9 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 30x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 30x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 30x + x2 = 0 + -9 30x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 30x + x2 = -9 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = -9 + 225 Reorder the terms: 225 + 30x + x2 = -9 + 225 Combine like terms: -9 + 225 = 216 225 + 30x + x2 = 216 Factor a perfect square on the left side: (x + 15)(x + 15) = 216 Calculate the square root of the right side: 14.696938457 Break this problem into two subproblems by setting (x + 15) equal to 14.696938457 and -14.696938457.Subproblem 1
x + 15 = 14.696938457 Simplifying x + 15 = 14.696938457 Reorder the terms: 15 + x = 14.696938457 Solving 15 + x = 14.696938457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 14.696938457 + -15 Combine like terms: 15 + -15 = 0 0 + x = 14.696938457 + -15 x = 14.696938457 + -15 Combine like terms: 14.696938457 + -15 = -0.303061543 x = -0.303061543 Simplifying x = -0.303061543Subproblem 2
x + 15 = -14.696938457 Simplifying x + 15 = -14.696938457 Reorder the terms: 15 + x = -14.696938457 Solving 15 + x = -14.696938457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -14.696938457 + -15 Combine like terms: 15 + -15 = 0 0 + x = -14.696938457 + -15 x = -14.696938457 + -15 Combine like terms: -14.696938457 + -15 = -29.696938457 x = -29.696938457 Simplifying x = -29.696938457Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.303061543, -29.696938457}
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