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Simplifying 6x + 9x2 = 5 Solving 6x + 9x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 6x + 9x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 6x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.5555555556 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + 0.6666666667x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + 0.6666666667x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + 0.6666666667x + x2 = 0 + 0.5555555556 0.6666666667x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 0.6666666667x + x2 = 0.5555555556 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 0.5555555556 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 0.5555555556 + 0.1111111112 Combine like terms: 0.5555555556 + 0.1111111112 = 0.6666666668 0.1111111112 + 0.6666666667x + x2 = 0.6666666668 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 0.6666666668 Calculate the square root of the right side: 0.816496581 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 0.816496581 and -0.816496581.Subproblem 1
x + 0.3333333334 = 0.816496581 Simplifying x + 0.3333333334 = 0.816496581 Reorder the terms: 0.3333333334 + x = 0.816496581 Solving 0.3333333334 + x = 0.816496581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 0.816496581 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 0.816496581 + -0.3333333334 x = 0.816496581 + -0.3333333334 Combine like terms: 0.816496581 + -0.3333333334 = 0.4831632476 x = 0.4831632476 Simplifying x = 0.4831632476Subproblem 2
x + 0.3333333334 = -0.816496581 Simplifying x + 0.3333333334 = -0.816496581 Reorder the terms: 0.3333333334 + x = -0.816496581 Solving 0.3333333334 + x = -0.816496581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -0.816496581 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -0.816496581 + -0.3333333334 x = -0.816496581 + -0.3333333334 Combine like terms: -0.816496581 + -0.3333333334 = -1.1498299144 x = -1.1498299144 Simplifying x = -1.1498299144Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4831632476, -1.1498299144}
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