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Simplifying (x + 9)(x + 9) = 648 Reorder the terms: (9 + x)(x + 9) = 648 Reorder the terms: (9 + x)(9 + x) = 648 Multiply (9 + x) * (9 + x) (9(9 + x) + x(9 + x)) = 648 ((9 * 9 + x * 9) + x(9 + x)) = 648 ((81 + 9x) + x(9 + x)) = 648 (81 + 9x + (9 * x + x * x)) = 648 (81 + 9x + (9x + x2)) = 648 Combine like terms: 9x + 9x = 18x (81 + 18x + x2) = 648 Solving 81 + 18x + x2 = 648 Solving for variable 'x'. Reorder the terms: 81 + -648 + 18x + x2 = 648 + -648 Combine like terms: 81 + -648 = -567 -567 + 18x + x2 = 648 + -648 Combine like terms: 648 + -648 = 0 -567 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '567' to each side of the equation. -567 + 18x + 567 + x2 = 0 + 567 Reorder the terms: -567 + 567 + 18x + x2 = 0 + 567 Combine like terms: -567 + 567 = 0 0 + 18x + x2 = 0 + 567 18x + x2 = 0 + 567 Combine like terms: 0 + 567 = 567 18x + x2 = 567 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 567 + 81 Reorder the terms: 81 + 18x + x2 = 567 + 81 Combine like terms: 567 + 81 = 648 81 + 18x + x2 = 648 Factor a perfect square on the left side: (x + 9)(x + 9) = 648 Calculate the square root of the right side: 25.455844123 Break this problem into two subproblems by setting (x + 9) equal to 25.455844123 and -25.455844123.Subproblem 1
x + 9 = 25.455844123 Simplifying x + 9 = 25.455844123 Reorder the terms: 9 + x = 25.455844123 Solving 9 + x = 25.455844123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 25.455844123 + -9 Combine like terms: 9 + -9 = 0 0 + x = 25.455844123 + -9 x = 25.455844123 + -9 Combine like terms: 25.455844123 + -9 = 16.455844123 x = 16.455844123 Simplifying x = 16.455844123Subproblem 2
x + 9 = -25.455844123 Simplifying x + 9 = -25.455844123 Reorder the terms: 9 + x = -25.455844123 Solving 9 + x = -25.455844123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -25.455844123 + -9 Combine like terms: 9 + -9 = 0 0 + x = -25.455844123 + -9 x = -25.455844123 + -9 Combine like terms: -25.455844123 + -9 = -34.455844123 x = -34.455844123 Simplifying x = -34.455844123Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.455844123, -34.455844123}
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