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Simplifying x * 9(x + 17) = -1 Reorder the terms: x * 9(17 + x) = -1 Reorder the terms for easier multiplication: 9x(17 + x) = -1 (17 * 9x + x * 9x) = -1 (153x + 9x2) = -1 Solving 153x + 9x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + 153x + 9x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 153x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.1111111111 + 17x + x2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + 17x + -0.1111111111 + x2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + 17x + x2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + 17x + x2 = 0 + -0.1111111111 17x + x2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 17x + x2 = -0.1111111111 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = -0.1111111111 + 72.25 Reorder the terms: 72.25 + 17x + x2 = -0.1111111111 + 72.25 Combine like terms: -0.1111111111 + 72.25 = 72.1388888889 72.25 + 17x + x2 = 72.1388888889 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 72.1388888889 Calculate the square root of the right side: 8.493461537 Break this problem into two subproblems by setting (x + 8.5) equal to 8.493461537 and -8.493461537.Subproblem 1
x + 8.5 = 8.493461537 Simplifying x + 8.5 = 8.493461537 Reorder the terms: 8.5 + x = 8.493461537 Solving 8.5 + x = 8.493461537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 8.493461537 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 8.493461537 + -8.5 x = 8.493461537 + -8.5 Combine like terms: 8.493461537 + -8.5 = -0.006538463 x = -0.006538463 Simplifying x = -0.006538463Subproblem 2
x + 8.5 = -8.493461537 Simplifying x + 8.5 = -8.493461537 Reorder the terms: 8.5 + x = -8.493461537 Solving 8.5 + x = -8.493461537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -8.493461537 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -8.493461537 + -8.5 x = -8.493461537 + -8.5 Combine like terms: -8.493461537 + -8.5 = -16.993461537 x = -16.993461537 Simplifying x = -16.993461537Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.006538463, -16.993461537}
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