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Simplifying 9x(x + 2) + 5 = 3x(x + 1) Reorder the terms: 9x(2 + x) + 5 = 3x(x + 1) (2 * 9x + x * 9x) + 5 = 3x(x + 1) (18x + 9x2) + 5 = 3x(x + 1) Reorder the terms: 5 + 18x + 9x2 = 3x(x + 1) Reorder the terms: 5 + 18x + 9x2 = 3x(1 + x) 5 + 18x + 9x2 = (1 * 3x + x * 3x) 5 + 18x + 9x2 = (3x + 3x2) Solving 5 + 18x + 9x2 = 3x + 3x2 Solving for variable 'x'. Reorder the terms: 5 + 18x + -3x + 9x2 + -3x2 = 3x + 3x2 + -3x + -3x2 Combine like terms: 18x + -3x = 15x 5 + 15x + 9x2 + -3x2 = 3x + 3x2 + -3x + -3x2 Combine like terms: 9x2 + -3x2 = 6x2 5 + 15x + 6x2 = 3x + 3x2 + -3x + -3x2 Reorder the terms: 5 + 15x + 6x2 = 3x + -3x + 3x2 + -3x2 Combine like terms: 3x + -3x = 0 5 + 15x + 6x2 = 0 + 3x2 + -3x2 5 + 15x + 6x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 5 + 15x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + 2.5x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + 2.5x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + 2.5x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + 2.5x + x2 = 0 + -0.8333333333 2.5x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 2.5x + x2 = -0.8333333333 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = -0.8333333333 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -0.8333333333 + 1.5625 Combine like terms: -0.8333333333 + 1.5625 = 0.7291666667 1.5625 + 2.5x + x2 = 0.7291666667 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 0.7291666667 Calculate the square root of the right side: 0.853912564 Break this problem into two subproblems by setting (x + 1.25) equal to 0.853912564 and -0.853912564.Subproblem 1
x + 1.25 = 0.853912564 Simplifying x + 1.25 = 0.853912564 Reorder the terms: 1.25 + x = 0.853912564 Solving 1.25 + x = 0.853912564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 0.853912564 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 0.853912564 + -1.25 x = 0.853912564 + -1.25 Combine like terms: 0.853912564 + -1.25 = -0.396087436 x = -0.396087436 Simplifying x = -0.396087436Subproblem 2
x + 1.25 = -0.853912564 Simplifying x + 1.25 = -0.853912564 Reorder the terms: 1.25 + x = -0.853912564 Solving 1.25 + x = -0.853912564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -0.853912564 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -0.853912564 + -1.25 x = -0.853912564 + -1.25 Combine like terms: -0.853912564 + -1.25 = -2.103912564 x = -2.103912564 Simplifying x = -2.103912564Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.396087436, -2.103912564}
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