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Simplifying 7x2 = 75x + -22 Reorder the terms: 7x2 = -22 + 75x Solving 7x2 = -22 + 75x Solving for variable 'x'. Reorder the terms: 22 + -75x + 7x2 = -22 + 75x + 22 + -75x Reorder the terms: 22 + -75x + 7x2 = -22 + 22 + 75x + -75x Combine like terms: -22 + 22 = 0 22 + -75x + 7x2 = 0 + 75x + -75x 22 + -75x + 7x2 = 75x + -75x Combine like terms: 75x + -75x = 0 22 + -75x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 3.142857143 + -10.71428571x + x2 = 0 Move the constant term to the right: Add '-3.142857143' to each side of the equation. 3.142857143 + -10.71428571x + -3.142857143 + x2 = 0 + -3.142857143 Reorder the terms: 3.142857143 + -3.142857143 + -10.71428571x + x2 = 0 + -3.142857143 Combine like terms: 3.142857143 + -3.142857143 = 0.000000000 0.000000000 + -10.71428571x + x2 = 0 + -3.142857143 -10.71428571x + x2 = 0 + -3.142857143 Combine like terms: 0 + -3.142857143 = -3.142857143 -10.71428571x + x2 = -3.142857143 The x term is -10.71428571x. Take half its coefficient (-5.357142855). Square it (28.69897957) and add it to both sides. Add '28.69897957' to each side of the equation. -10.71428571x + 28.69897957 + x2 = -3.142857143 + 28.69897957 Reorder the terms: 28.69897957 + -10.71428571x + x2 = -3.142857143 + 28.69897957 Combine like terms: -3.142857143 + 28.69897957 = 25.556122427 28.69897957 + -10.71428571x + x2 = 25.556122427 Factor a perfect square on the left side: (x + -5.357142855)(x + -5.357142855) = 25.556122427 Calculate the square root of the right side: 5.055306363 Break this problem into two subproblems by setting (x + -5.357142855) equal to 5.055306363 and -5.055306363.Subproblem 1
x + -5.357142855 = 5.055306363 Simplifying x + -5.357142855 = 5.055306363 Reorder the terms: -5.357142855 + x = 5.055306363 Solving -5.357142855 + x = 5.055306363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.357142855' to each side of the equation. -5.357142855 + 5.357142855 + x = 5.055306363 + 5.357142855 Combine like terms: -5.357142855 + 5.357142855 = 0.000000000 0.000000000 + x = 5.055306363 + 5.357142855 x = 5.055306363 + 5.357142855 Combine like terms: 5.055306363 + 5.357142855 = 10.412449218 x = 10.412449218 Simplifying x = 10.412449218Subproblem 2
x + -5.357142855 = -5.055306363 Simplifying x + -5.357142855 = -5.055306363 Reorder the terms: -5.357142855 + x = -5.055306363 Solving -5.357142855 + x = -5.055306363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.357142855' to each side of the equation. -5.357142855 + 5.357142855 + x = -5.055306363 + 5.357142855 Combine like terms: -5.357142855 + 5.357142855 = 0.000000000 0.000000000 + x = -5.055306363 + 5.357142855 x = -5.055306363 + 5.357142855 Combine like terms: -5.055306363 + 5.357142855 = 0.301836492 x = 0.301836492 Simplifying x = 0.301836492Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.412449218, 0.301836492}
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