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Simplifying 16x2 + -3x + 255 = 321 Reorder the terms: 255 + -3x + 16x2 = 321 Solving 255 + -3x + 16x2 = 321 Solving for variable 'x'. Reorder the terms: 255 + -321 + -3x + 16x2 = 321 + -321 Combine like terms: 255 + -321 = -66 -66 + -3x + 16x2 = 321 + -321 Combine like terms: 321 + -321 = 0 -66 + -3x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -4.125 + -0.1875x + x2 = 0 Move the constant term to the right: Add '4.125' to each side of the equation. -4.125 + -0.1875x + 4.125 + x2 = 0 + 4.125 Reorder the terms: -4.125 + 4.125 + -0.1875x + x2 = 0 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + -0.1875x + x2 = 0 + 4.125 -0.1875x + x2 = 0 + 4.125 Combine like terms: 0 + 4.125 = 4.125 -0.1875x + x2 = 4.125 The x term is -0.1875x. Take half its coefficient (-0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. -0.1875x + 0.0087890625 + x2 = 4.125 + 0.0087890625 Reorder the terms: 0.0087890625 + -0.1875x + x2 = 4.125 + 0.0087890625 Combine like terms: 4.125 + 0.0087890625 = 4.1337890625 0.0087890625 + -0.1875x + x2 = 4.1337890625 Factor a perfect square on the left side: (x + -0.09375)(x + -0.09375) = 4.1337890625 Calculate the square root of the right side: 2.033172167 Break this problem into two subproblems by setting (x + -0.09375) equal to 2.033172167 and -2.033172167.Subproblem 1
x + -0.09375 = 2.033172167 Simplifying x + -0.09375 = 2.033172167 Reorder the terms: -0.09375 + x = 2.033172167 Solving -0.09375 + x = 2.033172167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + x = 2.033172167 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + x = 2.033172167 + 0.09375 x = 2.033172167 + 0.09375 Combine like terms: 2.033172167 + 0.09375 = 2.126922167 x = 2.126922167 Simplifying x = 2.126922167Subproblem 2
x + -0.09375 = -2.033172167 Simplifying x + -0.09375 = -2.033172167 Reorder the terms: -0.09375 + x = -2.033172167 Solving -0.09375 + x = -2.033172167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + x = -2.033172167 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + x = -2.033172167 + 0.09375 x = -2.033172167 + 0.09375 Combine like terms: -2.033172167 + 0.09375 = -1.939422167 x = -1.939422167 Simplifying x = -1.939422167Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.126922167, -1.939422167}
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