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Simplifying 9x2 = 18x + 10 Reorder the terms: 9x2 = 10 + 18x Solving 9x2 = 10 + 18x Solving for variable 'x'. Reorder the terms: -10 + -18x + 9x2 = 10 + 18x + -10 + -18x Reorder the terms: -10 + -18x + 9x2 = 10 + -10 + 18x + -18x Combine like terms: 10 + -10 = 0 -10 + -18x + 9x2 = 0 + 18x + -18x -10 + -18x + 9x2 = 18x + -18x Combine like terms: 18x + -18x = 0 -10 + -18x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.111111111 + -2x + x2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + -2x + 1.111111111 + x2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + -2x + x2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + -2x + x2 = 0 + 1.111111111 -2x + x2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 -2x + x2 = 1.111111111 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 1.111111111 + 1 Reorder the terms: 1 + -2x + x2 = 1.111111111 + 1 Combine like terms: 1.111111111 + 1 = 2.111111111 1 + -2x + x2 = 2.111111111 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.111111111 Calculate the square root of the right side: 1.452966314 Break this problem into two subproblems by setting (x + -1) equal to 1.452966314 and -1.452966314.Subproblem 1
x + -1 = 1.452966314 Simplifying x + -1 = 1.452966314 Reorder the terms: -1 + x = 1.452966314 Solving -1 + x = 1.452966314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.452966314 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.452966314 + 1 x = 1.452966314 + 1 Combine like terms: 1.452966314 + 1 = 2.452966314 x = 2.452966314 Simplifying x = 2.452966314Subproblem 2
x + -1 = -1.452966314 Simplifying x + -1 = -1.452966314 Reorder the terms: -1 + x = -1.452966314 Solving -1 + x = -1.452966314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.452966314 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.452966314 + 1 x = -1.452966314 + 1 Combine like terms: -1.452966314 + 1 = -0.452966314 x = -0.452966314 Simplifying x = -0.452966314Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.452966314, -0.452966314}
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