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Simplifying 9x2 + 5x = 21 Reorder the terms: 5x + 9x2 = 21 Solving 5x + 9x2 = 21 Solving for variable 'x'. Reorder the terms: -21 + 5x + 9x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 5x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.333333333 + 0.5555555556x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 0.5555555556x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 0.5555555556x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 0.5555555556x + x2 = 0 + 2.333333333 0.5555555556x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 0.5555555556x + x2 = 2.333333333 The x term is 0.5555555556x. Take half its coefficient (0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. 0.5555555556x + 0.07716049384 + x2 = 2.333333333 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556x + x2 = 2.333333333 + 0.07716049384 Combine like terms: 2.333333333 + 0.07716049384 = 2.41049382684 0.07716049384 + 0.5555555556x + x2 = 2.41049382684 Factor a perfect square on the left side: (x + 0.2777777778)(x + 0.2777777778) = 2.41049382684 Calculate the square root of the right side: 1.552576512 Break this problem into two subproblems by setting (x + 0.2777777778) equal to 1.552576512 and -1.552576512.Subproblem 1
x + 0.2777777778 = 1.552576512 Simplifying x + 0.2777777778 = 1.552576512 Reorder the terms: 0.2777777778 + x = 1.552576512 Solving 0.2777777778 + x = 1.552576512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = 1.552576512 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = 1.552576512 + -0.2777777778 x = 1.552576512 + -0.2777777778 Combine like terms: 1.552576512 + -0.2777777778 = 1.2747987342 x = 1.2747987342 Simplifying x = 1.2747987342Subproblem 2
x + 0.2777777778 = -1.552576512 Simplifying x + 0.2777777778 = -1.552576512 Reorder the terms: 0.2777777778 + x = -1.552576512 Solving 0.2777777778 + x = -1.552576512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = -1.552576512 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = -1.552576512 + -0.2777777778 x = -1.552576512 + -0.2777777778 Combine like terms: -1.552576512 + -0.2777777778 = -1.8303542898 x = -1.8303542898 Simplifying x = -1.8303542898Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2747987342, -1.8303542898}
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