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Simplifying 1 + 9x(x + -8) = 10x(5 + x) Reorder the terms: 1 + 9x(-8 + x) = 10x(5 + x) 1 + (-8 * 9x + x * 9x) = 10x(5 + x) 1 + (-72x + 9x2) = 10x(5 + x) 1 + -72x + 9x2 = (5 * 10x + x * 10x) 1 + -72x + 9x2 = (50x + 10x2) Solving 1 + -72x + 9x2 = 50x + 10x2 Solving for variable 'x'. Reorder the terms: 1 + -72x + -50x + 9x2 + -10x2 = 50x + 10x2 + -50x + -10x2 Combine like terms: -72x + -50x = -122x 1 + -122x + 9x2 + -10x2 = 50x + 10x2 + -50x + -10x2 Combine like terms: 9x2 + -10x2 = -1x2 1 + -122x + -1x2 = 50x + 10x2 + -50x + -10x2 Reorder the terms: 1 + -122x + -1x2 = 50x + -50x + 10x2 + -10x2 Combine like terms: 50x + -50x = 0 1 + -122x + -1x2 = 0 + 10x2 + -10x2 1 + -122x + -1x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 1 + -122x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + 122x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 122x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 122x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 122x + x2 = 0 + 1 122x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 122x + x2 = 1 The x term is 122x. Take half its coefficient (61). Square it (3721) and add it to both sides. Add '3721' to each side of the equation. 122x + 3721 + x2 = 1 + 3721 Reorder the terms: 3721 + 122x + x2 = 1 + 3721 Combine like terms: 1 + 3721 = 3722 3721 + 122x + x2 = 3722 Factor a perfect square on the left side: (x + 61)(x + 61) = 3722 Calculate the square root of the right side: 61.008196171 Break this problem into two subproblems by setting (x + 61) equal to 61.008196171 and -61.008196171.Subproblem 1
x + 61 = 61.008196171 Simplifying x + 61 = 61.008196171 Reorder the terms: 61 + x = 61.008196171 Solving 61 + x = 61.008196171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-61' to each side of the equation. 61 + -61 + x = 61.008196171 + -61 Combine like terms: 61 + -61 = 0 0 + x = 61.008196171 + -61 x = 61.008196171 + -61 Combine like terms: 61.008196171 + -61 = 0.008196171 x = 0.008196171 Simplifying x = 0.008196171Subproblem 2
x + 61 = -61.008196171 Simplifying x + 61 = -61.008196171 Reorder the terms: 61 + x = -61.008196171 Solving 61 + x = -61.008196171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-61' to each side of the equation. 61 + -61 + x = -61.008196171 + -61 Combine like terms: 61 + -61 = 0 0 + x = -61.008196171 + -61 x = -61.008196171 + -61 Combine like terms: -61.008196171 + -61 = -122.008196171 x = -122.008196171 Simplifying x = -122.008196171Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.008196171, -122.008196171}
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