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Simplifying x = 4x2 + 76x + -1160 Reorder the terms: x = -1160 + 76x + 4x2 Solving x = -1160 + 76x + 4x2 Solving for variable 'x'. Reorder the terms: 1160 + x + -76x + -4x2 = -1160 + 76x + 4x2 + 1160 + -76x + -4x2 Combine like terms: x + -76x = -75x 1160 + -75x + -4x2 = -1160 + 76x + 4x2 + 1160 + -76x + -4x2 Reorder the terms: 1160 + -75x + -4x2 = -1160 + 1160 + 76x + -76x + 4x2 + -4x2 Combine like terms: -1160 + 1160 = 0 1160 + -75x + -4x2 = 0 + 76x + -76x + 4x2 + -4x2 1160 + -75x + -4x2 = 76x + -76x + 4x2 + -4x2 Combine like terms: 76x + -76x = 0 1160 + -75x + -4x2 = 0 + 4x2 + -4x2 1160 + -75x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 1160 + -75x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -290 + 18.75x + x2 = 0 Move the constant term to the right: Add '290' to each side of the equation. -290 + 18.75x + 290 + x2 = 0 + 290 Reorder the terms: -290 + 290 + 18.75x + x2 = 0 + 290 Combine like terms: -290 + 290 = 0 0 + 18.75x + x2 = 0 + 290 18.75x + x2 = 0 + 290 Combine like terms: 0 + 290 = 290 18.75x + x2 = 290 The x term is 18.75x. Take half its coefficient (9.375). Square it (87.890625) and add it to both sides. Add '87.890625' to each side of the equation. 18.75x + 87.890625 + x2 = 290 + 87.890625 Reorder the terms: 87.890625 + 18.75x + x2 = 290 + 87.890625 Combine like terms: 290 + 87.890625 = 377.890625 87.890625 + 18.75x + x2 = 377.890625 Factor a perfect square on the left side: (x + 9.375)(x + 9.375) = 377.890625 Calculate the square root of the right side: 19.43940907 Break this problem into two subproblems by setting (x + 9.375) equal to 19.43940907 and -19.43940907.Subproblem 1
x + 9.375 = 19.43940907 Simplifying x + 9.375 = 19.43940907 Reorder the terms: 9.375 + x = 19.43940907 Solving 9.375 + x = 19.43940907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.375' to each side of the equation. 9.375 + -9.375 + x = 19.43940907 + -9.375 Combine like terms: 9.375 + -9.375 = 0.000 0.000 + x = 19.43940907 + -9.375 x = 19.43940907 + -9.375 Combine like terms: 19.43940907 + -9.375 = 10.06440907 x = 10.06440907 Simplifying x = 10.06440907Subproblem 2
x + 9.375 = -19.43940907 Simplifying x + 9.375 = -19.43940907 Reorder the terms: 9.375 + x = -19.43940907 Solving 9.375 + x = -19.43940907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.375' to each side of the equation. 9.375 + -9.375 + x = -19.43940907 + -9.375 Combine like terms: 9.375 + -9.375 = 0.000 0.000 + x = -19.43940907 + -9.375 x = -19.43940907 + -9.375 Combine like terms: -19.43940907 + -9.375 = -28.81440907 x = -28.81440907 Simplifying x = -28.81440907Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.06440907, -28.81440907}
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