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Simplifying 7x2 + -76x + 30 = 0 Reorder the terms: 30 + -76x + 7x2 = 0 Solving 30 + -76x + 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'. 4.285714286 + -10.85714286x + x2 = 0 Move the constant term to the right: Add '-4.285714286' to each side of the equation. 4.285714286 + -10.85714286x + -4.285714286 + x2 = 0 + -4.285714286 Reorder the terms: 4.285714286 + -4.285714286 + -10.85714286x + x2 = 0 + -4.285714286 Combine like terms: 4.285714286 + -4.285714286 = 0.000000000 0.000000000 + -10.85714286x + x2 = 0 + -4.285714286 -10.85714286x + x2 = 0 + -4.285714286 Combine like terms: 0 + -4.285714286 = -4.285714286 -10.85714286x + x2 = -4.285714286 The x term is -10.85714286x. Take half its coefficient (-5.42857143). Square it (29.46938777) and add it to both sides. Add '29.46938777' to each side of the equation. -10.85714286x + 29.46938777 + x2 = -4.285714286 + 29.46938777 Reorder the terms: 29.46938777 + -10.85714286x + x2 = -4.285714286 + 29.46938777 Combine like terms: -4.285714286 + 29.46938777 = 25.183673484 29.46938777 + -10.85714286x + x2 = 25.183673484 Factor a perfect square on the left side: (x + -5.42857143)(x + -5.42857143) = 25.183673484 Calculate the square root of the right side: 5.018333736 Break this problem into two subproblems by setting (x + -5.42857143) equal to 5.018333736 and -5.018333736.Subproblem 1
x + -5.42857143 = 5.018333736 Simplifying x + -5.42857143 = 5.018333736 Reorder the terms: -5.42857143 + x = 5.018333736 Solving -5.42857143 + x = 5.018333736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.42857143' to each side of the equation. -5.42857143 + 5.42857143 + x = 5.018333736 + 5.42857143 Combine like terms: -5.42857143 + 5.42857143 = 0.00000000 0.00000000 + x = 5.018333736 + 5.42857143 x = 5.018333736 + 5.42857143 Combine like terms: 5.018333736 + 5.42857143 = 10.446905166 x = 10.446905166 Simplifying x = 10.446905166Subproblem 2
x + -5.42857143 = -5.018333736 Simplifying x + -5.42857143 = -5.018333736 Reorder the terms: -5.42857143 + x = -5.018333736 Solving -5.42857143 + x = -5.018333736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.42857143' to each side of the equation. -5.42857143 + 5.42857143 + x = -5.018333736 + 5.42857143 Combine like terms: -5.42857143 + 5.42857143 = 0.00000000 0.00000000 + x = -5.018333736 + 5.42857143 x = -5.018333736 + 5.42857143 Combine like terms: -5.018333736 + 5.42857143 = 0.410237694 x = 0.410237694 Simplifying x = 0.410237694Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.446905166, 0.410237694}
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