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Simplifying x(9x + -5) = 40 Reorder the terms: x(-5 + 9x) = 40 (-5 * x + 9x * x) = 40 (-5x + 9x2) = 40 Solving -5x + 9x2 = 40 Solving for variable 'x'. Reorder the terms: -40 + -5x + 9x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + -5x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -4.444444444 + -0.5555555556x + x2 = 0 Move the constant term to the right: Add '4.444444444' to each side of the equation. -4.444444444 + -0.5555555556x + 4.444444444 + x2 = 0 + 4.444444444 Reorder the terms: -4.444444444 + 4.444444444 + -0.5555555556x + x2 = 0 + 4.444444444 Combine like terms: -4.444444444 + 4.444444444 = 0.000000000 0.000000000 + -0.5555555556x + x2 = 0 + 4.444444444 -0.5555555556x + x2 = 0 + 4.444444444 Combine like terms: 0 + 4.444444444 = 4.444444444 -0.5555555556x + x2 = 4.444444444 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 = 4.444444444 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556x + x2 = 4.444444444 + 0.07716049384 Combine like terms: 4.444444444 + 0.07716049384 = 4.52160493784 0.07716049384 + -0.5555555556x + x2 = 4.52160493784 Factor a perfect square on the left side: (x + -0.2777777778)(x + -0.2777777778) = 4.52160493784 Calculate the square root of the right side: 2.126406579 Break this problem into two subproblems by setting (x + -0.2777777778) equal to 2.126406579 and -2.126406579.Subproblem 1
x + -0.2777777778 = 2.126406579 Simplifying x + -0.2777777778 = 2.126406579 Reorder the terms: -0.2777777778 + x = 2.126406579 Solving -0.2777777778 + x = 2.126406579 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 = 2.126406579 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = 2.126406579 + 0.2777777778 x = 2.126406579 + 0.2777777778 Combine like terms: 2.126406579 + 0.2777777778 = 2.4041843568 x = 2.4041843568 Simplifying x = 2.4041843568Subproblem 2
x + -0.2777777778 = -2.126406579 Simplifying x + -0.2777777778 = -2.126406579 Reorder the terms: -0.2777777778 + x = -2.126406579 Solving -0.2777777778 + x = -2.126406579 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 = -2.126406579 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = -2.126406579 + 0.2777777778 x = -2.126406579 + 0.2777777778 Combine like terms: -2.126406579 + 0.2777777778 = -1.8486288012 x = -1.8486288012 Simplifying x = -1.8486288012Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4041843568, -1.8486288012}
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