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Simplifying 9x(x + -2) = 4(x + 2) Reorder the terms: 9x(-2 + x) = 4(x + 2) (-2 * 9x + x * 9x) = 4(x + 2) (-18x + 9x2) = 4(x + 2) Reorder the terms: -18x + 9x2 = 4(2 + x) -18x + 9x2 = (2 * 4 + x * 4) -18x + 9x2 = (8 + 4x) Solving -18x + 9x2 = 8 + 4x Solving for variable 'x'. Reorder the terms: -8 + -18x + -4x + 9x2 = 8 + 4x + -8 + -4x Combine like terms: -18x + -4x = -22x -8 + -22x + 9x2 = 8 + 4x + -8 + -4x Reorder the terms: -8 + -22x + 9x2 = 8 + -8 + 4x + -4x Combine like terms: 8 + -8 = 0 -8 + -22x + 9x2 = 0 + 4x + -4x -8 + -22x + 9x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -8 + -22x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.8888888889 + -2.444444444x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -2.444444444x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -2.444444444x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -2.444444444x + x2 = 0 + 0.8888888889 -2.444444444x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -2.444444444x + x2 = 0.8888888889 The x term is -2.444444444x. Take half its coefficient (-1.222222222). Square it (1.493827160) and add it to both sides. Add '1.493827160' to each side of the equation. -2.444444444x + 1.493827160 + x2 = 0.8888888889 + 1.493827160 Reorder the terms: 1.493827160 + -2.444444444x + x2 = 0.8888888889 + 1.493827160 Combine like terms: 0.8888888889 + 1.493827160 = 2.3827160489 1.493827160 + -2.444444444x + x2 = 2.3827160489 Factor a perfect square on the left side: (x + -1.222222222)(x + -1.222222222) = 2.3827160489 Calculate the square root of the right side: 1.543604888 Break this problem into two subproblems by setting (x + -1.222222222) equal to 1.543604888 and -1.543604888.Subproblem 1
x + -1.222222222 = 1.543604888 Simplifying x + -1.222222222 = 1.543604888 Reorder the terms: -1.222222222 + x = 1.543604888 Solving -1.222222222 + x = 1.543604888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.222222222' to each side of the equation. -1.222222222 + 1.222222222 + x = 1.543604888 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + x = 1.543604888 + 1.222222222 x = 1.543604888 + 1.222222222 Combine like terms: 1.543604888 + 1.222222222 = 2.76582711 x = 2.76582711 Simplifying x = 2.76582711Subproblem 2
x + -1.222222222 = -1.543604888 Simplifying x + -1.222222222 = -1.543604888 Reorder the terms: -1.222222222 + x = -1.543604888 Solving -1.222222222 + x = -1.543604888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.222222222' to each side of the equation. -1.222222222 + 1.222222222 + x = -1.543604888 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + x = -1.543604888 + 1.222222222 x = -1.543604888 + 1.222222222 Combine like terms: -1.543604888 + 1.222222222 = -0.321382666 x = -0.321382666 Simplifying x = -0.321382666Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.76582711, -0.321382666}
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