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Simplifying 16x2 + 3x + 2 = 80 Reorder the terms: 2 + 3x + 16x2 = 80 Solving 2 + 3x + 16x2 = 80 Solving for variable 'x'. Reorder the terms: 2 + -80 + 3x + 16x2 = 80 + -80 Combine like terms: 2 + -80 = -78 -78 + 3x + 16x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -78 + 3x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -4.875 + 0.1875x + x2 = 0 Move the constant term to the right: Add '4.875' to each side of the equation. -4.875 + 0.1875x + 4.875 + x2 = 0 + 4.875 Reorder the terms: -4.875 + 4.875 + 0.1875x + x2 = 0 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + 0.1875x + x2 = 0 + 4.875 0.1875x + x2 = 0 + 4.875 Combine like terms: 0 + 4.875 = 4.875 0.1875x + x2 = 4.875 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 = 4.875 + 0.0087890625 Reorder the terms: 0.0087890625 + 0.1875x + x2 = 4.875 + 0.0087890625 Combine like terms: 4.875 + 0.0087890625 = 4.8837890625 0.0087890625 + 0.1875x + x2 = 4.8837890625 Factor a perfect square on the left side: (x + 0.09375)(x + 0.09375) = 4.8837890625 Calculate the square root of the right side: 2.209929651 Break this problem into two subproblems by setting (x + 0.09375) equal to 2.209929651 and -2.209929651.Subproblem 1
x + 0.09375 = 2.209929651 Simplifying x + 0.09375 = 2.209929651 Reorder the terms: 0.09375 + x = 2.209929651 Solving 0.09375 + x = 2.209929651 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 = 2.209929651 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = 2.209929651 + -0.09375 x = 2.209929651 + -0.09375 Combine like terms: 2.209929651 + -0.09375 = 2.116179651 x = 2.116179651 Simplifying x = 2.116179651Subproblem 2
x + 0.09375 = -2.209929651 Simplifying x + 0.09375 = -2.209929651 Reorder the terms: 0.09375 + x = -2.209929651 Solving 0.09375 + x = -2.209929651 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 = -2.209929651 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = -2.209929651 + -0.09375 x = -2.209929651 + -0.09375 Combine like terms: -2.209929651 + -0.09375 = -2.303679651 x = -2.303679651 Simplifying x = -2.303679651Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.116179651, -2.303679651}
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