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Simplifying 7x2 + -36x + 6 = 0 Reorder the terms: 6 + -36x + 7x2 = 0 Solving 6 + -36x + 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'. 0.8571428571 + -5.142857143x + x2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + -5.142857143x + -0.8571428571 + x2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + -5.142857143x + x2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + -5.142857143x + x2 = 0 + -0.8571428571 -5.142857143x + x2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 -5.142857143x + x2 = -0.8571428571 The x term is -5.142857143x. Take half its coefficient (-2.571428572). Square it (6.612244901) and add it to both sides. Add '6.612244901' to each side of the equation. -5.142857143x + 6.612244901 + x2 = -0.8571428571 + 6.612244901 Reorder the terms: 6.612244901 + -5.142857143x + x2 = -0.8571428571 + 6.612244901 Combine like terms: -0.8571428571 + 6.612244901 = 5.7551020439 6.612244901 + -5.142857143x + x2 = 5.7551020439 Factor a perfect square on the left side: (x + -2.571428572)(x + -2.571428572) = 5.7551020439 Calculate the square root of the right side: 2.398979375 Break this problem into two subproblems by setting (x + -2.571428572) equal to 2.398979375 and -2.398979375.Subproblem 1
x + -2.571428572 = 2.398979375 Simplifying x + -2.571428572 = 2.398979375 Reorder the terms: -2.571428572 + x = 2.398979375 Solving -2.571428572 + x = 2.398979375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.571428572' to each side of the equation. -2.571428572 + 2.571428572 + x = 2.398979375 + 2.571428572 Combine like terms: -2.571428572 + 2.571428572 = 0.000000000 0.000000000 + x = 2.398979375 + 2.571428572 x = 2.398979375 + 2.571428572 Combine like terms: 2.398979375 + 2.571428572 = 4.970407947 x = 4.970407947 Simplifying x = 4.970407947Subproblem 2
x + -2.571428572 = -2.398979375 Simplifying x + -2.571428572 = -2.398979375 Reorder the terms: -2.571428572 + x = -2.398979375 Solving -2.571428572 + x = -2.398979375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.571428572' to each side of the equation. -2.571428572 + 2.571428572 + x = -2.398979375 + 2.571428572 Combine like terms: -2.571428572 + 2.571428572 = 0.000000000 0.000000000 + x = -2.398979375 + 2.571428572 x = -2.398979375 + 2.571428572 Combine like terms: -2.398979375 + 2.571428572 = 0.172449197 x = 0.172449197 Simplifying x = 0.172449197Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.970407947, 0.172449197}
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