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Simplifying (x + 6)(x + 9) = 20 Reorder the terms: (6 + x)(x + 9) = 20 Reorder the terms: (6 + x)(9 + x) = 20 Multiply (6 + x) * (9 + x) (6(9 + x) + x(9 + x)) = 20 ((9 * 6 + x * 6) + x(9 + x)) = 20 ((54 + 6x) + x(9 + x)) = 20 (54 + 6x + (9 * x + x * x)) = 20 (54 + 6x + (9x + x2)) = 20 Combine like terms: 6x + 9x = 15x (54 + 15x + x2) = 20 Solving 54 + 15x + x2 = 20 Solving for variable 'x'. Reorder the terms: 54 + -20 + 15x + x2 = 20 + -20 Combine like terms: 54 + -20 = 34 34 + 15x + x2 = 20 + -20 Combine like terms: 20 + -20 = 0 34 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-34' to each side of the equation. 34 + 15x + -34 + x2 = 0 + -34 Reorder the terms: 34 + -34 + 15x + x2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + 15x + x2 = 0 + -34 15x + x2 = 0 + -34 Combine like terms: 0 + -34 = -34 15x + x2 = -34 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = -34 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -34 + 56.25 Combine like terms: -34 + 56.25 = 22.25 56.25 + 15x + x2 = 22.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (x + 7.5) equal to 4.716990566 and -4.716990566.Subproblem 1
x + 7.5 = 4.716990566 Simplifying x + 7.5 = 4.716990566 Reorder the terms: 7.5 + x = 4.716990566 Solving 7.5 + x = 4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 4.716990566 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 4.716990566 + -7.5 x = 4.716990566 + -7.5 Combine like terms: 4.716990566 + -7.5 = -2.783009434 x = -2.783009434 Simplifying x = -2.783009434Subproblem 2
x + 7.5 = -4.716990566 Simplifying x + 7.5 = -4.716990566 Reorder the terms: 7.5 + x = -4.716990566 Solving 7.5 + x = -4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -4.716990566 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -4.716990566 + -7.5 x = -4.716990566 + -7.5 Combine like terms: -4.716990566 + -7.5 = -12.216990566 x = -12.216990566 Simplifying x = -12.216990566Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.783009434, -12.216990566}
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