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Simplifying 16x2 + 368x + -2035 = 0 Reorder the terms: -2035 + 368x + 16x2 = 0 Solving -2035 + 368x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -127.1875 + 23x + x2 = 0 Move the constant term to the right: Add '127.1875' to each side of the equation. -127.1875 + 23x + 127.1875 + x2 = 0 + 127.1875 Reorder the terms: -127.1875 + 127.1875 + 23x + x2 = 0 + 127.1875 Combine like terms: -127.1875 + 127.1875 = 0.0000 0.0000 + 23x + x2 = 0 + 127.1875 23x + x2 = 0 + 127.1875 Combine like terms: 0 + 127.1875 = 127.1875 23x + x2 = 127.1875 The x term is 23x. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23x + 132.25 + x2 = 127.1875 + 132.25 Reorder the terms: 132.25 + 23x + x2 = 127.1875 + 132.25 Combine like terms: 127.1875 + 132.25 = 259.4375 132.25 + 23x + x2 = 259.4375 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 259.4375 Calculate the square root of the right side: 16.107063668 Break this problem into two subproblems by setting (x + 11.5) equal to 16.107063668 and -16.107063668.Subproblem 1
x + 11.5 = 16.107063668 Simplifying x + 11.5 = 16.107063668 Reorder the terms: 11.5 + x = 16.107063668 Solving 11.5 + x = 16.107063668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = 16.107063668 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 16.107063668 + -11.5 x = 16.107063668 + -11.5 Combine like terms: 16.107063668 + -11.5 = 4.607063668 x = 4.607063668 Simplifying x = 4.607063668Subproblem 2
x + 11.5 = -16.107063668 Simplifying x + 11.5 = -16.107063668 Reorder the terms: 11.5 + x = -16.107063668 Solving 11.5 + x = -16.107063668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = -16.107063668 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -16.107063668 + -11.5 x = -16.107063668 + -11.5 Combine like terms: -16.107063668 + -11.5 = -27.607063668 x = -27.607063668 Simplifying x = -27.607063668Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.607063668, -27.607063668}
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