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Simplifying 4x2 + -85x + 18 = 0 Reorder the terms: 18 + -85x + 4x2 = 0 Solving 18 + -85x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4.5 + -21.25x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -21.25x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -21.25x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -21.25x + x2 = 0 + -4.5 -21.25x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -21.25x + x2 = -4.5 The x term is -21.25x. Take half its coefficient (-10.625). Square it (112.890625) and add it to both sides. Add '112.890625' to each side of the equation. -21.25x + 112.890625 + x2 = -4.5 + 112.890625 Reorder the terms: 112.890625 + -21.25x + x2 = -4.5 + 112.890625 Combine like terms: -4.5 + 112.890625 = 108.390625 112.890625 + -21.25x + x2 = 108.390625 Factor a perfect square on the left side: (x + -10.625)(x + -10.625) = 108.390625 Calculate the square root of the right side: 10.411081836 Break this problem into two subproblems by setting (x + -10.625) equal to 10.411081836 and -10.411081836.Subproblem 1
x + -10.625 = 10.411081836 Simplifying x + -10.625 = 10.411081836 Reorder the terms: -10.625 + x = 10.411081836 Solving -10.625 + x = 10.411081836 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.625' to each side of the equation. -10.625 + 10.625 + x = 10.411081836 + 10.625 Combine like terms: -10.625 + 10.625 = 0.000 0.000 + x = 10.411081836 + 10.625 x = 10.411081836 + 10.625 Combine like terms: 10.411081836 + 10.625 = 21.036081836 x = 21.036081836 Simplifying x = 21.036081836Subproblem 2
x + -10.625 = -10.411081836 Simplifying x + -10.625 = -10.411081836 Reorder the terms: -10.625 + x = -10.411081836 Solving -10.625 + x = -10.411081836 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.625' to each side of the equation. -10.625 + 10.625 + x = -10.411081836 + 10.625 Combine like terms: -10.625 + 10.625 = 0.000 0.000 + x = -10.411081836 + 10.625 x = -10.411081836 + 10.625 Combine like terms: -10.411081836 + 10.625 = 0.213918164 x = 0.213918164 Simplifying x = 0.213918164Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.036081836, 0.213918164}
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