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Simplifying 7x2 + 43x + -760 = 0 Reorder the terms: -760 + 43x + 7x2 = 0 Solving -760 + 43x + 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'. -108.5714286 + 6.142857143x + x2 = 0 Move the constant term to the right: Add '108.5714286' to each side of the equation. -108.5714286 + 6.142857143x + 108.5714286 + x2 = 0 + 108.5714286 Reorder the terms: -108.5714286 + 108.5714286 + 6.142857143x + x2 = 0 + 108.5714286 Combine like terms: -108.5714286 + 108.5714286 = 0.0000000 0.0000000 + 6.142857143x + x2 = 0 + 108.5714286 6.142857143x + x2 = 0 + 108.5714286 Combine like terms: 0 + 108.5714286 = 108.5714286 6.142857143x + x2 = 108.5714286 The x term is 6.142857143x. Take half its coefficient (3.071428572). Square it (9.433673473) and add it to both sides. Add '9.433673473' to each side of the equation. 6.142857143x + 9.433673473 + x2 = 108.5714286 + 9.433673473 Reorder the terms: 9.433673473 + 6.142857143x + x2 = 108.5714286 + 9.433673473 Combine like terms: 108.5714286 + 9.433673473 = 118.005102073 9.433673473 + 6.142857143x + x2 = 118.005102073 Factor a perfect square on the left side: (x + 3.071428572)(x + 3.071428572) = 118.005102073 Calculate the square root of the right side: 10.863015331 Break this problem into two subproblems by setting (x + 3.071428572) equal to 10.863015331 and -10.863015331.Subproblem 1
x + 3.071428572 = 10.863015331 Simplifying x + 3.071428572 = 10.863015331 Reorder the terms: 3.071428572 + x = 10.863015331 Solving 3.071428572 + x = 10.863015331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.071428572' to each side of the equation. 3.071428572 + -3.071428572 + x = 10.863015331 + -3.071428572 Combine like terms: 3.071428572 + -3.071428572 = 0.000000000 0.000000000 + x = 10.863015331 + -3.071428572 x = 10.863015331 + -3.071428572 Combine like terms: 10.863015331 + -3.071428572 = 7.791586759 x = 7.791586759 Simplifying x = 7.791586759Subproblem 2
x + 3.071428572 = -10.863015331 Simplifying x + 3.071428572 = -10.863015331 Reorder the terms: 3.071428572 + x = -10.863015331 Solving 3.071428572 + x = -10.863015331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.071428572' to each side of the equation. 3.071428572 + -3.071428572 + x = -10.863015331 + -3.071428572 Combine like terms: 3.071428572 + -3.071428572 = 0.000000000 0.000000000 + x = -10.863015331 + -3.071428572 x = -10.863015331 + -3.071428572 Combine like terms: -10.863015331 + -3.071428572 = -13.934443903 x = -13.934443903 Simplifying x = -13.934443903Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.791586759, -13.934443903}
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