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Simplifying 3 + -9x(x + 3) + -5 = 3 + 3(9 + -3x) + -81 Reorder the terms: 3 + -9x(3 + x) + -5 = 3 + 3(9 + -3x) + -81 3 + (3 * -9x + x * -9x) + -5 = 3 + 3(9 + -3x) + -81 3 + (-27x + -9x2) + -5 = 3 + 3(9 + -3x) + -81 Reorder the terms: 3 + -5 + -27x + -9x2 = 3 + 3(9 + -3x) + -81 Combine like terms: 3 + -5 = -2 -2 + -27x + -9x2 = 3 + 3(9 + -3x) + -81 -2 + -27x + -9x2 = 3 + (9 * 3 + -3x * 3) + -81 -2 + -27x + -9x2 = 3 + (27 + -9x) + -81 Reorder the terms: -2 + -27x + -9x2 = 3 + 27 + -81 + -9x Combine like terms: 3 + 27 = 30 -2 + -27x + -9x2 = 30 + -81 + -9x Combine like terms: 30 + -81 = -51 -2 + -27x + -9x2 = -51 + -9x Solving -2 + -27x + -9x2 = -51 + -9x Solving for variable 'x'. Reorder the terms: -2 + 51 + -27x + 9x + -9x2 = -51 + -9x + 51 + 9x Combine like terms: -2 + 51 = 49 49 + -27x + 9x + -9x2 = -51 + -9x + 51 + 9x Combine like terms: -27x + 9x = -18x 49 + -18x + -9x2 = -51 + -9x + 51 + 9x Reorder the terms: 49 + -18x + -9x2 = -51 + 51 + -9x + 9x Combine like terms: -51 + 51 = 0 49 + -18x + -9x2 = 0 + -9x + 9x 49 + -18x + -9x2 = -9x + 9x Combine like terms: -9x + 9x = 0 49 + -18x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -5.444444444 + 2x + x2 = 0 Move the constant term to the right: Add '5.444444444' to each side of the equation. -5.444444444 + 2x + 5.444444444 + x2 = 0 + 5.444444444 Reorder the terms: -5.444444444 + 5.444444444 + 2x + x2 = 0 + 5.444444444 Combine like terms: -5.444444444 + 5.444444444 = 0.000000000 0.000000000 + 2x + x2 = 0 + 5.444444444 2x + x2 = 0 + 5.444444444 Combine like terms: 0 + 5.444444444 = 5.444444444 2x + x2 = 5.444444444 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 5.444444444 + 1 Reorder the terms: 1 + 2x + x2 = 5.444444444 + 1 Combine like terms: 5.444444444 + 1 = 6.444444444 1 + 2x + x2 = 6.444444444 Factor a perfect square on the left side: (x + 1)(x + 1) = 6.444444444 Calculate the square root of the right side: 2.538591035 Break this problem into two subproblems by setting (x + 1) equal to 2.538591035 and -2.538591035.Subproblem 1
x + 1 = 2.538591035 Simplifying x + 1 = 2.538591035 Reorder the terms: 1 + x = 2.538591035 Solving 1 + x = 2.538591035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.538591035 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.538591035 + -1 x = 2.538591035 + -1 Combine like terms: 2.538591035 + -1 = 1.538591035 x = 1.538591035 Simplifying x = 1.538591035Subproblem 2
x + 1 = -2.538591035 Simplifying x + 1 = -2.538591035 Reorder the terms: 1 + x = -2.538591035 Solving 1 + x = -2.538591035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.538591035 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.538591035 + -1 x = -2.538591035 + -1 Combine like terms: -2.538591035 + -1 = -3.538591035 x = -3.538591035 Simplifying x = -3.538591035Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.538591035, -3.538591035}
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