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Simplifying 9x2 + 18x = 14 Reorder the terms: 18x + 9x2 = 14 Solving 18x + 9x2 = 14 Solving for variable 'x'. Reorder the terms: -14 + 18x + 9x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 18x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.555555556 + 2x + x2 = 0 Move the constant term to the right: Add '1.555555556' to each side of the equation. -1.555555556 + 2x + 1.555555556 + x2 = 0 + 1.555555556 Reorder the terms: -1.555555556 + 1.555555556 + 2x + x2 = 0 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + 2x + x2 = 0 + 1.555555556 2x + x2 = 0 + 1.555555556 Combine like terms: 0 + 1.555555556 = 1.555555556 2x + x2 = 1.555555556 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 = 1.555555556 + 1 Reorder the terms: 1 + 2x + x2 = 1.555555556 + 1 Combine like terms: 1.555555556 + 1 = 2.555555556 1 + 2x + x2 = 2.555555556 Factor a perfect square on the left side: (x + 1)(x + 1) = 2.555555556 Calculate the square root of the right side: 1.598610508 Break this problem into two subproblems by setting (x + 1) equal to 1.598610508 and -1.598610508.Subproblem 1
x + 1 = 1.598610508 Simplifying x + 1 = 1.598610508 Reorder the terms: 1 + x = 1.598610508 Solving 1 + x = 1.598610508 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 = 1.598610508 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.598610508 + -1 x = 1.598610508 + -1 Combine like terms: 1.598610508 + -1 = 0.598610508 x = 0.598610508 Simplifying x = 0.598610508Subproblem 2
x + 1 = -1.598610508 Simplifying x + 1 = -1.598610508 Reorder the terms: 1 + x = -1.598610508 Solving 1 + x = -1.598610508 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 = -1.598610508 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.598610508 + -1 x = -1.598610508 + -1 Combine like terms: -1.598610508 + -1 = -2.598610508 x = -2.598610508 Simplifying x = -2.598610508Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.598610508, -2.598610508}
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