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Simplifying 1.6x2 + -12.6x + 8.4 = 0 Reorder the terms: 8.4 + -12.6x + 1.6x2 = 0 Solving 8.4 + -12.6x + 1.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.6 the coefficient of the squared term: Divide each side by '1.6'. 5.25 + -7.875x + x2 = 0 Move the constant term to the right: Add '-5.25' to each side of the equation. 5.25 + -7.875x + -5.25 + x2 = 0 + -5.25 Reorder the terms: 5.25 + -5.25 + -7.875x + x2 = 0 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + -7.875x + x2 = 0 + -5.25 -7.875x + x2 = 0 + -5.25 Combine like terms: 0 + -5.25 = -5.25 -7.875x + x2 = -5.25 The x term is -7.875x. Take half its coefficient (-3.9375). Square it (15.50390625) and add it to both sides. Add '15.50390625' to each side of the equation. -7.875x + 15.50390625 + x2 = -5.25 + 15.50390625 Reorder the terms: 15.50390625 + -7.875x + x2 = -5.25 + 15.50390625 Combine like terms: -5.25 + 15.50390625 = 10.25390625 15.50390625 + -7.875x + x2 = 10.25390625 Factor a perfect square on the left side: (x + -3.9375)(x + -3.9375) = 10.25390625 Calculate the square root of the right side: 3.202172114 Break this problem into two subproblems by setting (x + -3.9375) equal to 3.202172114 and -3.202172114.Subproblem 1
x + -3.9375 = 3.202172114 Simplifying x + -3.9375 = 3.202172114 Reorder the terms: -3.9375 + x = 3.202172114 Solving -3.9375 + x = 3.202172114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.9375' to each side of the equation. -3.9375 + 3.9375 + x = 3.202172114 + 3.9375 Combine like terms: -3.9375 + 3.9375 = 0.0000 0.0000 + x = 3.202172114 + 3.9375 x = 3.202172114 + 3.9375 Combine like terms: 3.202172114 + 3.9375 = 7.139672114 x = 7.139672114 Simplifying x = 7.139672114Subproblem 2
x + -3.9375 = -3.202172114 Simplifying x + -3.9375 = -3.202172114 Reorder the terms: -3.9375 + x = -3.202172114 Solving -3.9375 + x = -3.202172114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.9375' to each side of the equation. -3.9375 + 3.9375 + x = -3.202172114 + 3.9375 Combine like terms: -3.9375 + 3.9375 = 0.0000 0.0000 + x = -3.202172114 + 3.9375 x = -3.202172114 + 3.9375 Combine like terms: -3.202172114 + 3.9375 = 0.735327886 x = 0.735327886 Simplifying x = 0.735327886Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.139672114, 0.735327886}
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