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Simplifying 16x2 + 77x = 17 + 6x Reorder the terms: 77x + 16x2 = 17 + 6x Solving 77x + 16x2 = 17 + 6x Solving for variable 'x'. Reorder the terms: -17 + 77x + -6x + 16x2 = 17 + 6x + -17 + -6x Combine like terms: 77x + -6x = 71x -17 + 71x + 16x2 = 17 + 6x + -17 + -6x Reorder the terms: -17 + 71x + 16x2 = 17 + -17 + 6x + -6x Combine like terms: 17 + -17 = 0 -17 + 71x + 16x2 = 0 + 6x + -6x -17 + 71x + 16x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -17 + 71x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.0625 + 4.4375x + x2 = 0 Move the constant term to the right: Add '1.0625' to each side of the equation. -1.0625 + 4.4375x + 1.0625 + x2 = 0 + 1.0625 Reorder the terms: -1.0625 + 1.0625 + 4.4375x + x2 = 0 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + 4.4375x + x2 = 0 + 1.0625 4.4375x + x2 = 0 + 1.0625 Combine like terms: 0 + 1.0625 = 1.0625 4.4375x + x2 = 1.0625 The x term is 4.4375x. Take half its coefficient (2.21875). Square it (4.922851563) and add it to both sides. Add '4.922851563' to each side of the equation. 4.4375x + 4.922851563 + x2 = 1.0625 + 4.922851563 Reorder the terms: 4.922851563 + 4.4375x + x2 = 1.0625 + 4.922851563 Combine like terms: 1.0625 + 4.922851563 = 5.985351563 4.922851563 + 4.4375x + x2 = 5.985351563 Factor a perfect square on the left side: (x + 2.21875)(x + 2.21875) = 5.985351563 Calculate the square root of the right side: 2.446497816 Break this problem into two subproblems by setting (x + 2.21875) equal to 2.446497816 and -2.446497816.Subproblem 1
x + 2.21875 = 2.446497816 Simplifying x + 2.21875 = 2.446497816 Reorder the terms: 2.21875 + x = 2.446497816 Solving 2.21875 + x = 2.446497816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.21875' to each side of the equation. 2.21875 + -2.21875 + x = 2.446497816 + -2.21875 Combine like terms: 2.21875 + -2.21875 = 0.00000 0.00000 + x = 2.446497816 + -2.21875 x = 2.446497816 + -2.21875 Combine like terms: 2.446497816 + -2.21875 = 0.227747816 x = 0.227747816 Simplifying x = 0.227747816Subproblem 2
x + 2.21875 = -2.446497816 Simplifying x + 2.21875 = -2.446497816 Reorder the terms: 2.21875 + x = -2.446497816 Solving 2.21875 + x = -2.446497816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.21875' to each side of the equation. 2.21875 + -2.21875 + x = -2.446497816 + -2.21875 Combine like terms: 2.21875 + -2.21875 = 0.00000 0.00000 + x = -2.446497816 + -2.21875 x = -2.446497816 + -2.21875 Combine like terms: -2.446497816 + -2.21875 = -4.665247816 x = -4.665247816 Simplifying x = -4.665247816Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.227747816, -4.665247816}
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