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Simplifying x(9x + -5) = 13 Reorder the terms: x(-5 + 9x) = 13 (-5 * x + 9x * x) = 13 (-5x + 9x2) = 13 Solving -5x + 9x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + -5x + 9x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -5x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.444444444 + -0.5555555556x + x2 = 0 Move the constant term to the right: Add '1.444444444' to each side of the equation. -1.444444444 + -0.5555555556x + 1.444444444 + x2 = 0 + 1.444444444 Reorder the terms: -1.444444444 + 1.444444444 + -0.5555555556x + x2 = 0 + 1.444444444 Combine like terms: -1.444444444 + 1.444444444 = 0.000000000 0.000000000 + -0.5555555556x + x2 = 0 + 1.444444444 -0.5555555556x + x2 = 0 + 1.444444444 Combine like terms: 0 + 1.444444444 = 1.444444444 -0.5555555556x + x2 = 1.444444444 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 = 1.444444444 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556x + x2 = 1.444444444 + 0.07716049384 Combine like terms: 1.444444444 + 0.07716049384 = 1.52160493784 0.07716049384 + -0.5555555556x + x2 = 1.52160493784 Factor a perfect square on the left side: (x + -0.2777777778)(x + -0.2777777778) = 1.52160493784 Calculate the square root of the right side: 1.233533517 Break this problem into two subproblems by setting (x + -0.2777777778) equal to 1.233533517 and -1.233533517.Subproblem 1
x + -0.2777777778 = 1.233533517 Simplifying x + -0.2777777778 = 1.233533517 Reorder the terms: -0.2777777778 + x = 1.233533517 Solving -0.2777777778 + x = 1.233533517 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 = 1.233533517 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = 1.233533517 + 0.2777777778 x = 1.233533517 + 0.2777777778 Combine like terms: 1.233533517 + 0.2777777778 = 1.5113112948 x = 1.5113112948 Simplifying x = 1.5113112948Subproblem 2
x + -0.2777777778 = -1.233533517 Simplifying x + -0.2777777778 = -1.233533517 Reorder the terms: -0.2777777778 + x = -1.233533517 Solving -0.2777777778 + x = -1.233533517 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 = -1.233533517 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = -1.233533517 + 0.2777777778 x = -1.233533517 + 0.2777777778 Combine like terms: -1.233533517 + 0.2777777778 = -0.9557557392 x = -0.9557557392 Simplifying x = -0.9557557392Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5113112948, -0.9557557392}
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