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Simplifying 9x + 5 = 4(x + 2) * 5x Reorder the terms: 5 + 9x = 4(x + 2) * 5x Reorder the terms: 5 + 9x = 4(2 + x) * 5x Reorder the terms for easier multiplication: 5 + 9x = 4 * 5x(2 + x) Multiply 4 * 5 5 + 9x = 20x(2 + x) 5 + 9x = (2 * 20x + x * 20x) 5 + 9x = (40x + 20x2) Solving 5 + 9x = 40x + 20x2 Solving for variable 'x'. Combine like terms: 9x + -40x = -31x 5 + -31x + -20x2 = 40x + 20x2 + -40x + -20x2 Reorder the terms: 5 + -31x + -20x2 = 40x + -40x + 20x2 + -20x2 Combine like terms: 40x + -40x = 0 5 + -31x + -20x2 = 0 + 20x2 + -20x2 5 + -31x + -20x2 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 5 + -31x + -20x2 = 0 Begin completing the square. Divide all terms by -20 the coefficient of the squared term: Divide each side by '-20'. -0.25 + 1.55x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 1.55x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 1.55x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 1.55x + x2 = 0 + 0.25 1.55x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 1.55x + x2 = 0.25 The x term is 1.55x. Take half its coefficient (0.775). Square it (0.600625) and add it to both sides. Add '0.600625' to each side of the equation. 1.55x + 0.600625 + x2 = 0.25 + 0.600625 Reorder the terms: 0.600625 + 1.55x + x2 = 0.25 + 0.600625 Combine like terms: 0.25 + 0.600625 = 0.850625 0.600625 + 1.55x + x2 = 0.850625 Factor a perfect square on the left side: (x + 0.775)(x + 0.775) = 0.850625 Calculate the square root of the right side: 0.922293337 Break this problem into two subproblems by setting (x + 0.775) equal to 0.922293337 and -0.922293337.Subproblem 1
x + 0.775 = 0.922293337 Simplifying x + 0.775 = 0.922293337 Reorder the terms: 0.775 + x = 0.922293337 Solving 0.775 + x = 0.922293337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.775' to each side of the equation. 0.775 + -0.775 + x = 0.922293337 + -0.775 Combine like terms: 0.775 + -0.775 = 0.000 0.000 + x = 0.922293337 + -0.775 x = 0.922293337 + -0.775 Combine like terms: 0.922293337 + -0.775 = 0.147293337 x = 0.147293337 Simplifying x = 0.147293337Subproblem 2
x + 0.775 = -0.922293337 Simplifying x + 0.775 = -0.922293337 Reorder the terms: 0.775 + x = -0.922293337 Solving 0.775 + x = -0.922293337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.775' to each side of the equation. 0.775 + -0.775 + x = -0.922293337 + -0.775 Combine like terms: 0.775 + -0.775 = 0.000 0.000 + x = -0.922293337 + -0.775 x = -0.922293337 + -0.775 Combine like terms: -0.922293337 + -0.775 = -1.697293337 x = -1.697293337 Simplifying x = -1.697293337Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.147293337, -1.697293337}
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