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Simplifying 81 + -1(3x + 5) = 3(x + 9) * x Reorder the terms: 81 + -1(5 + 3x) = 3(x + 9) * x 81 + (5 * -1 + 3x * -1) = 3(x + 9) * x 81 + (-5 + -3x) = 3(x + 9) * x Combine like terms: 81 + -5 = 76 76 + -3x = 3(x + 9) * x Reorder the terms: 76 + -3x = 3(9 + x) * x Reorder the terms for easier multiplication: 76 + -3x = 3x(9 + x) 76 + -3x = (9 * 3x + x * 3x) 76 + -3x = (27x + 3x2) Solving 76 + -3x = 27x + 3x2 Solving for variable 'x'. Combine like terms: -3x + -27x = -30x 76 + -30x + -3x2 = 27x + 3x2 + -27x + -3x2 Reorder the terms: 76 + -30x + -3x2 = 27x + -27x + 3x2 + -3x2 Combine like terms: 27x + -27x = 0 76 + -30x + -3x2 = 0 + 3x2 + -3x2 76 + -30x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 76 + -30x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -25.33333333 + 10x + x2 = 0 Move the constant term to the right: Add '25.33333333' to each side of the equation. -25.33333333 + 10x + 25.33333333 + x2 = 0 + 25.33333333 Reorder the terms: -25.33333333 + 25.33333333 + 10x + x2 = 0 + 25.33333333 Combine like terms: -25.33333333 + 25.33333333 = 0.00000000 0.00000000 + 10x + x2 = 0 + 25.33333333 10x + x2 = 0 + 25.33333333 Combine like terms: 0 + 25.33333333 = 25.33333333 10x + x2 = 25.33333333 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 25.33333333 + 25 Reorder the terms: 25 + 10x + x2 = 25.33333333 + 25 Combine like terms: 25.33333333 + 25 = 50.33333333 25 + 10x + x2 = 50.33333333 Factor a perfect square on the left side: (x + 5)(x + 5) = 50.33333333 Calculate the square root of the right side: 7.094598884 Break this problem into two subproblems by setting (x + 5) equal to 7.094598884 and -7.094598884.Subproblem 1
x + 5 = 7.094598884 Simplifying x + 5 = 7.094598884 Reorder the terms: 5 + x = 7.094598884 Solving 5 + x = 7.094598884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 7.094598884 + -5 Combine like terms: 5 + -5 = 0 0 + x = 7.094598884 + -5 x = 7.094598884 + -5 Combine like terms: 7.094598884 + -5 = 2.094598884 x = 2.094598884 Simplifying x = 2.094598884Subproblem 2
x + 5 = -7.094598884 Simplifying x + 5 = -7.094598884 Reorder the terms: 5 + x = -7.094598884 Solving 5 + x = -7.094598884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -7.094598884 + -5 Combine like terms: 5 + -5 = 0 0 + x = -7.094598884 + -5 x = -7.094598884 + -5 Combine like terms: -7.094598884 + -5 = -12.094598884 x = -12.094598884 Simplifying x = -12.094598884Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.094598884, -12.094598884}
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