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Simplifying 6.6x2 + -169x + -2855 = 0 Reorder the terms: -2855 + -169x + 6.6x2 = 0 Solving -2855 + -169x + 6.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6.6 the coefficient of the squared term: Divide each side by '6.6'. -432.5757576 + -25.60606061x + x2 = 0 Move the constant term to the right: Add '432.5757576' to each side of the equation. -432.5757576 + -25.60606061x + 432.5757576 + x2 = 0 + 432.5757576 Reorder the terms: -432.5757576 + 432.5757576 + -25.60606061x + x2 = 0 + 432.5757576 Combine like terms: -432.5757576 + 432.5757576 = 0.0000000 0.0000000 + -25.60606061x + x2 = 0 + 432.5757576 -25.60606061x + x2 = 0 + 432.5757576 Combine like terms: 0 + 432.5757576 = 432.5757576 -25.60606061x + x2 = 432.5757576 The x term is -25.60606061x. Take half its coefficient (-12.80303031). Square it (163.9175851) and add it to both sides. Add '163.9175851' to each side of the equation. -25.60606061x + 163.9175851 + x2 = 432.5757576 + 163.9175851 Reorder the terms: 163.9175851 + -25.60606061x + x2 = 432.5757576 + 163.9175851 Combine like terms: 432.5757576 + 163.9175851 = 596.4933427 163.9175851 + -25.60606061x + x2 = 596.4933427 Factor a perfect square on the left side: (x + -12.80303031)(x + -12.80303031) = 596.4933427 Calculate the square root of the right side: 24.423213194 Break this problem into two subproblems by setting (x + -12.80303031) equal to 24.423213194 and -24.423213194.Subproblem 1
x + -12.80303031 = 24.423213194 Simplifying x + -12.80303031 = 24.423213194 Reorder the terms: -12.80303031 + x = 24.423213194 Solving -12.80303031 + x = 24.423213194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.80303031' to each side of the equation. -12.80303031 + 12.80303031 + x = 24.423213194 + 12.80303031 Combine like terms: -12.80303031 + 12.80303031 = 0.00000000 0.00000000 + x = 24.423213194 + 12.80303031 x = 24.423213194 + 12.80303031 Combine like terms: 24.423213194 + 12.80303031 = 37.226243504 x = 37.226243504 Simplifying x = 37.226243504Subproblem 2
x + -12.80303031 = -24.423213194 Simplifying x + -12.80303031 = -24.423213194 Reorder the terms: -12.80303031 + x = -24.423213194 Solving -12.80303031 + x = -24.423213194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.80303031' to each side of the equation. -12.80303031 + 12.80303031 + x = -24.423213194 + 12.80303031 Combine like terms: -12.80303031 + 12.80303031 = 0.00000000 0.00000000 + x = -24.423213194 + 12.80303031 x = -24.423213194 + 12.80303031 Combine like terms: -24.423213194 + 12.80303031 = -11.620182884 x = -11.620182884 Simplifying x = -11.620182884Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.226243504, -11.620182884}
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