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Simplifying (x + -5)(9x + 4) = 1 Reorder the terms: (-5 + x)(9x + 4) = 1 Reorder the terms: (-5 + x)(4 + 9x) = 1 Multiply (-5 + x) * (4 + 9x) (-5(4 + 9x) + x(4 + 9x)) = 1 ((4 * -5 + 9x * -5) + x(4 + 9x)) = 1 ((-20 + -45x) + x(4 + 9x)) = 1 (-20 + -45x + (4 * x + 9x * x)) = 1 (-20 + -45x + (4x + 9x2)) = 1 Combine like terms: -45x + 4x = -41x (-20 + -41x + 9x2) = 1 Solving -20 + -41x + 9x2 = 1 Solving for variable 'x'. Reorder the terms: -20 + -1 + -41x + 9x2 = 1 + -1 Combine like terms: -20 + -1 = -21 -21 + -41x + 9x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -21 + -41x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.333333333 + -4.555555556x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -4.555555556x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -4.555555556x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -4.555555556x + x2 = 0 + 2.333333333 -4.555555556x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -4.555555556x + x2 = 2.333333333 The x term is -4.555555556x. Take half its coefficient (-2.277777778). Square it (5.188271606) and add it to both sides. Add '5.188271606' to each side of the equation. -4.555555556x + 5.188271606 + x2 = 2.333333333 + 5.188271606 Reorder the terms: 5.188271606 + -4.555555556x + x2 = 2.333333333 + 5.188271606 Combine like terms: 2.333333333 + 5.188271606 = 7.521604939 5.188271606 + -4.555555556x + x2 = 7.521604939 Factor a perfect square on the left side: (x + -2.277777778)(x + -2.277777778) = 7.521604939 Calculate the square root of the right side: 2.742554455 Break this problem into two subproblems by setting (x + -2.277777778) equal to 2.742554455 and -2.742554455.Subproblem 1
x + -2.277777778 = 2.742554455 Simplifying x + -2.277777778 = 2.742554455 Reorder the terms: -2.277777778 + x = 2.742554455 Solving -2.277777778 + x = 2.742554455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.277777778' to each side of the equation. -2.277777778 + 2.277777778 + x = 2.742554455 + 2.277777778 Combine like terms: -2.277777778 + 2.277777778 = 0.000000000 0.000000000 + x = 2.742554455 + 2.277777778 x = 2.742554455 + 2.277777778 Combine like terms: 2.742554455 + 2.277777778 = 5.020332233 x = 5.020332233 Simplifying x = 5.020332233Subproblem 2
x + -2.277777778 = -2.742554455 Simplifying x + -2.277777778 = -2.742554455 Reorder the terms: -2.277777778 + x = -2.742554455 Solving -2.277777778 + x = -2.742554455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.277777778' to each side of the equation. -2.277777778 + 2.277777778 + x = -2.742554455 + 2.277777778 Combine like terms: -2.277777778 + 2.277777778 = 0.000000000 0.000000000 + x = -2.742554455 + 2.277777778 x = -2.742554455 + 2.277777778 Combine like terms: -2.742554455 + 2.277777778 = -0.464776677 x = -0.464776677 Simplifying x = -0.464776677Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.020332233, -0.464776677}
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