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Simplifying 7x2 + -95x + -364 = 0 Reorder the terms: -364 + -95x + 7x2 = 0 Solving -364 + -95x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -52 + -13.57142857x + x2 = 0 Move the constant term to the right: Add '52' to each side of the equation. -52 + -13.57142857x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + -13.57142857x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -13.57142857x + x2 = 0 + 52 -13.57142857x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 -13.57142857x + x2 = 52 The x term is -13.57142857x. Take half its coefficient (-6.785714285). Square it (46.04591836) and add it to both sides. Add '46.04591836' to each side of the equation. -13.57142857x + 46.04591836 + x2 = 52 + 46.04591836 Reorder the terms: 46.04591836 + -13.57142857x + x2 = 52 + 46.04591836 Combine like terms: 52 + 46.04591836 = 98.04591836 46.04591836 + -13.57142857x + x2 = 98.04591836 Factor a perfect square on the left side: (x + -6.785714285)(x + -6.785714285) = 98.04591836 Calculate the square root of the right side: 9.901813892 Break this problem into two subproblems by setting (x + -6.785714285) equal to 9.901813892 and -9.901813892.Subproblem 1
x + -6.785714285 = 9.901813892 Simplifying x + -6.785714285 = 9.901813892 Reorder the terms: -6.785714285 + x = 9.901813892 Solving -6.785714285 + x = 9.901813892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.785714285' to each side of the equation. -6.785714285 + 6.785714285 + x = 9.901813892 + 6.785714285 Combine like terms: -6.785714285 + 6.785714285 = 0.000000000 0.000000000 + x = 9.901813892 + 6.785714285 x = 9.901813892 + 6.785714285 Combine like terms: 9.901813892 + 6.785714285 = 16.687528177 x = 16.687528177 Simplifying x = 16.687528177Subproblem 2
x + -6.785714285 = -9.901813892 Simplifying x + -6.785714285 = -9.901813892 Reorder the terms: -6.785714285 + x = -9.901813892 Solving -6.785714285 + x = -9.901813892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.785714285' to each side of the equation. -6.785714285 + 6.785714285 + x = -9.901813892 + 6.785714285 Combine like terms: -6.785714285 + 6.785714285 = 0.000000000 0.000000000 + x = -9.901813892 + 6.785714285 x = -9.901813892 + 6.785714285 Combine like terms: -9.901813892 + 6.785714285 = -3.116099607 x = -3.116099607 Simplifying x = -3.116099607Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.687528177, -3.116099607}
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