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Simplifying -400 = -1x(9x + 8) + -1 Reorder the terms: -400 = -1x(8 + 9x) + -1 -400 = (8 * -1x + 9x * -1x) + -1 -400 = (-8x + -9x2) + -1 Reorder the terms: -400 = -1 + -8x + -9x2 Solving -400 = -1 + -8x + -9x2 Solving for variable 'x'. Combine like terms: -400 + 1 = -399 -399 + 8x + 9x2 = -1 + -8x + -9x2 + 1 + 8x + 9x2 Reorder the terms: -399 + 8x + 9x2 = -1 + 1 + -8x + 8x + -9x2 + 9x2 Combine like terms: -1 + 1 = 0 -399 + 8x + 9x2 = 0 + -8x + 8x + -9x2 + 9x2 -399 + 8x + 9x2 = -8x + 8x + -9x2 + 9x2 Combine like terms: -8x + 8x = 0 -399 + 8x + 9x2 = 0 + -9x2 + 9x2 -399 + 8x + 9x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 0 -399 + 8x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -44.33333333 + 0.8888888889x + x2 = 0 Move the constant term to the right: Add '44.33333333' to each side of the equation. -44.33333333 + 0.8888888889x + 44.33333333 + x2 = 0 + 44.33333333 Reorder the terms: -44.33333333 + 44.33333333 + 0.8888888889x + x2 = 0 + 44.33333333 Combine like terms: -44.33333333 + 44.33333333 = 0.00000000 0.00000000 + 0.8888888889x + x2 = 0 + 44.33333333 0.8888888889x + x2 = 0 + 44.33333333 Combine like terms: 0 + 44.33333333 = 44.33333333 0.8888888889x + x2 = 44.33333333 The x term is 0.8888888889x. Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. 0.8888888889x + 0.1975308642 + x2 = 44.33333333 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889x + x2 = 44.33333333 + 0.1975308642 Combine like terms: 44.33333333 + 0.1975308642 = 44.5308641942 0.1975308642 + 0.8888888889x + x2 = 44.5308641942 Factor a perfect square on the left side: (x + 0.4444444445)(x + 0.4444444445) = 44.5308641942 Calculate the square root of the right side: 6.673145 Break this problem into two subproblems by setting (x + 0.4444444445) equal to 6.673145 and -6.673145.Subproblem 1
x + 0.4444444445 = 6.673145 Simplifying x + 0.4444444445 = 6.673145 Reorder the terms: 0.4444444445 + x = 6.673145 Solving 0.4444444445 + x = 6.673145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = 6.673145 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = 6.673145 + -0.4444444445 x = 6.673145 + -0.4444444445 Combine like terms: 6.673145 + -0.4444444445 = 6.2287005555 x = 6.2287005555 Simplifying x = 6.2287005555Subproblem 2
x + 0.4444444445 = -6.673145 Simplifying x + 0.4444444445 = -6.673145 Reorder the terms: 0.4444444445 + x = -6.673145 Solving 0.4444444445 + x = -6.673145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = -6.673145 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = -6.673145 + -0.4444444445 x = -6.673145 + -0.4444444445 Combine like terms: -6.673145 + -0.4444444445 = -7.1175894445 x = -7.1175894445 Simplifying x = -7.1175894445Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.2287005555, -7.1175894445}
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