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Simplifying 9x(x + 2) + 4 = 5x(x + 1) Reorder the terms: 9x(2 + x) + 4 = 5x(x + 1) (2 * 9x + x * 9x) + 4 = 5x(x + 1) (18x + 9x2) + 4 = 5x(x + 1) Reorder the terms: 4 + 18x + 9x2 = 5x(x + 1) Reorder the terms: 4 + 18x + 9x2 = 5x(1 + x) 4 + 18x + 9x2 = (1 * 5x + x * 5x) 4 + 18x + 9x2 = (5x + 5x2) Solving 4 + 18x + 9x2 = 5x + 5x2 Solving for variable 'x'. Reorder the terms: 4 + 18x + -5x + 9x2 + -5x2 = 5x + 5x2 + -5x + -5x2 Combine like terms: 18x + -5x = 13x 4 + 13x + 9x2 + -5x2 = 5x + 5x2 + -5x + -5x2 Combine like terms: 9x2 + -5x2 = 4x2 4 + 13x + 4x2 = 5x + 5x2 + -5x + -5x2 Reorder the terms: 4 + 13x + 4x2 = 5x + -5x + 5x2 + -5x2 Combine like terms: 5x + -5x = 0 4 + 13x + 4x2 = 0 + 5x2 + -5x2 4 + 13x + 4x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 4 + 13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1 + 3.25x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 3.25x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 3.25x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3.25x + x2 = 0 + -1 3.25x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 3.25x + x2 = -1 The x term is 3.25x. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25x + 2.640625 + x2 = -1 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = -1 + 2.640625 Combine like terms: -1 + 2.640625 = 1.640625 2.640625 + 3.25x + x2 = 1.640625 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (x + 1.625) equal to 1.280868846 and -1.280868846.Subproblem 1
x + 1.625 = 1.280868846 Simplifying x + 1.625 = 1.280868846 Reorder the terms: 1.625 + x = 1.280868846 Solving 1.625 + x = 1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 1.280868846 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 1.280868846 + -1.625 x = 1.280868846 + -1.625 Combine like terms: 1.280868846 + -1.625 = -0.344131154 x = -0.344131154 Simplifying x = -0.344131154Subproblem 2
x + 1.625 = -1.280868846 Simplifying x + 1.625 = -1.280868846 Reorder the terms: 1.625 + x = -1.280868846 Solving 1.625 + x = -1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -1.280868846 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -1.280868846 + -1.625 x = -1.280868846 + -1.625 Combine like terms: -1.280868846 + -1.625 = -2.905868846 x = -2.905868846 Simplifying x = -2.905868846Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.344131154, -2.905868846}
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