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Simplifying (x + 9)(x + 9) = 3 Reorder the terms: (9 + x)(x + 9) = 3 Reorder the terms: (9 + x)(9 + x) = 3 Multiply (9 + x) * (9 + x) (9(9 + x) + x(9 + x)) = 3 ((9 * 9 + x * 9) + x(9 + x)) = 3 ((81 + 9x) + x(9 + x)) = 3 (81 + 9x + (9 * x + x * x)) = 3 (81 + 9x + (9x + x2)) = 3 Combine like terms: 9x + 9x = 18x (81 + 18x + x2) = 3 Solving 81 + 18x + x2 = 3 Solving for variable 'x'. Reorder the terms: 81 + -3 + 18x + x2 = 3 + -3 Combine like terms: 81 + -3 = 78 78 + 18x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 78 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-78' to each side of the equation. 78 + 18x + -78 + x2 = 0 + -78 Reorder the terms: 78 + -78 + 18x + x2 = 0 + -78 Combine like terms: 78 + -78 = 0 0 + 18x + x2 = 0 + -78 18x + x2 = 0 + -78 Combine like terms: 0 + -78 = -78 18x + x2 = -78 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 = -78 + 81 Reorder the terms: 81 + 18x + x2 = -78 + 81 Combine like terms: -78 + 81 = 3 81 + 18x + x2 = 3 Factor a perfect square on the left side: (x + 9)(x + 9) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + 9) equal to 1.732050808 and -1.732050808.Subproblem 1
x + 9 = 1.732050808 Simplifying x + 9 = 1.732050808 Reorder the terms: 9 + x = 1.732050808 Solving 9 + x = 1.732050808 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 = 1.732050808 + -9 Combine like terms: 9 + -9 = 0 0 + x = 1.732050808 + -9 x = 1.732050808 + -9 Combine like terms: 1.732050808 + -9 = -7.267949192 x = -7.267949192 Simplifying x = -7.267949192Subproblem 2
x + 9 = -1.732050808 Simplifying x + 9 = -1.732050808 Reorder the terms: 9 + x = -1.732050808 Solving 9 + x = -1.732050808 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 = -1.732050808 + -9 Combine like terms: 9 + -9 = 0 0 + x = -1.732050808 + -9 x = -1.732050808 + -9 Combine like terms: -1.732050808 + -9 = -10.732050808 x = -10.732050808 Simplifying x = -10.732050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.267949192, -10.732050808}
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