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Simplifying 0 = -32x2 + 89x + 343 Reorder the terms: 0 = 343 + 89x + -32x2 Solving 0 = 343 + 89x + -32x2 Solving for variable 'x'. Combine like terms: 0 + -343 = -343 -343 + -89x + 32x2 = 343 + 89x + -32x2 + -343 + -89x + 32x2 Reorder the terms: -343 + -89x + 32x2 = 343 + -343 + 89x + -89x + -32x2 + 32x2 Combine like terms: 343 + -343 = 0 -343 + -89x + 32x2 = 0 + 89x + -89x + -32x2 + 32x2 -343 + -89x + 32x2 = 89x + -89x + -32x2 + 32x2 Combine like terms: 89x + -89x = 0 -343 + -89x + 32x2 = 0 + -32x2 + 32x2 -343 + -89x + 32x2 = -32x2 + 32x2 Combine like terms: -32x2 + 32x2 = 0 -343 + -89x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -10.71875 + -2.78125x + x2 = 0 Move the constant term to the right: Add '10.71875' to each side of the equation. -10.71875 + -2.78125x + 10.71875 + x2 = 0 + 10.71875 Reorder the terms: -10.71875 + 10.71875 + -2.78125x + x2 = 0 + 10.71875 Combine like terms: -10.71875 + 10.71875 = 0.00000 0.00000 + -2.78125x + x2 = 0 + 10.71875 -2.78125x + x2 = 0 + 10.71875 Combine like terms: 0 + 10.71875 = 10.71875 -2.78125x + x2 = 10.71875 The x term is -2.78125x. Take half its coefficient (-1.390625). Square it (1.933837891) and add it to both sides. Add '1.933837891' to each side of the equation. -2.78125x + 1.933837891 + x2 = 10.71875 + 1.933837891 Reorder the terms: 1.933837891 + -2.78125x + x2 = 10.71875 + 1.933837891 Combine like terms: 10.71875 + 1.933837891 = 12.652587891 1.933837891 + -2.78125x + x2 = 12.652587891 Factor a perfect square on the left side: (x + -1.390625)(x + -1.390625) = 12.652587891 Calculate the square root of the right side: 3.557047637 Break this problem into two subproblems by setting (x + -1.390625) equal to 3.557047637 and -3.557047637.Subproblem 1
x + -1.390625 = 3.557047637 Simplifying x + -1.390625 = 3.557047637 Reorder the terms: -1.390625 + x = 3.557047637 Solving -1.390625 + x = 3.557047637 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.390625' to each side of the equation. -1.390625 + 1.390625 + x = 3.557047637 + 1.390625 Combine like terms: -1.390625 + 1.390625 = 0.000000 0.000000 + x = 3.557047637 + 1.390625 x = 3.557047637 + 1.390625 Combine like terms: 3.557047637 + 1.390625 = 4.947672637 x = 4.947672637 Simplifying x = 4.947672637Subproblem 2
x + -1.390625 = -3.557047637 Simplifying x + -1.390625 = -3.557047637 Reorder the terms: -1.390625 + x = -3.557047637 Solving -1.390625 + x = -3.557047637 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.390625' to each side of the equation. -1.390625 + 1.390625 + x = -3.557047637 + 1.390625 Combine like terms: -1.390625 + 1.390625 = 0.000000 0.000000 + x = -3.557047637 + 1.390625 x = -3.557047637 + 1.390625 Combine like terms: -3.557047637 + 1.390625 = -2.166422637 x = -2.166422637 Simplifying x = -2.166422637Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.947672637, -2.166422637}
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