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Simplifying 0 = -9x2 + 6x + 5 Reorder the terms: 0 = 5 + 6x + -9x2 Solving 0 = 5 + 6x + -9x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -6x + 9x2 = 5 + 6x + -9x2 + -5 + -6x + 9x2 Reorder the terms: -5 + -6x + 9x2 = 5 + -5 + 6x + -6x + -9x2 + 9x2 Combine like terms: 5 + -5 = 0 -5 + -6x + 9x2 = 0 + 6x + -6x + -9x2 + 9x2 -5 + -6x + 9x2 = 6x + -6x + -9x2 + 9x2 Combine like terms: 6x + -6x = 0 -5 + -6x + 9x2 = 0 + -9x2 + 9x2 -5 + -6x + 9x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 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 = 1.1498299144 x = 1.1498299144 Simplifying x = 1.1498299144Subproblem 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 = -0.4831632476 x = -0.4831632476 Simplifying x = -0.4831632476Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1498299144, -0.4831632476}
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