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Simplifying 7x2 + 51x + 4 = 0 Reorder the terms: 4 + 51x + 7x2 = 0 Solving 4 + 51x + 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'. 0.5714285714 + 7.285714286x + x2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + 7.285714286x + -0.5714285714 + x2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + 7.285714286x + x2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + 7.285714286x + x2 = 0 + -0.5714285714 7.285714286x + x2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 7.285714286x + x2 = -0.5714285714 The x term is 7.285714286x. Take half its coefficient (3.642857143). Square it (13.27040816) and add it to both sides. Add '13.27040816' to each side of the equation. 7.285714286x + 13.27040816 + x2 = -0.5714285714 + 13.27040816 Reorder the terms: 13.27040816 + 7.285714286x + x2 = -0.5714285714 + 13.27040816 Combine like terms: -0.5714285714 + 13.27040816 = 12.6989795886 13.27040816 + 7.285714286x + x2 = 12.6989795886 Factor a perfect square on the left side: (x + 3.642857143)(x + 3.642857143) = 12.6989795886 Calculate the square root of the right side: 3.563562766 Break this problem into two subproblems by setting (x + 3.642857143) equal to 3.563562766 and -3.563562766.Subproblem 1
x + 3.642857143 = 3.563562766 Simplifying x + 3.642857143 = 3.563562766 Reorder the terms: 3.642857143 + x = 3.563562766 Solving 3.642857143 + x = 3.563562766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.642857143' to each side of the equation. 3.642857143 + -3.642857143 + x = 3.563562766 + -3.642857143 Combine like terms: 3.642857143 + -3.642857143 = 0.000000000 0.000000000 + x = 3.563562766 + -3.642857143 x = 3.563562766 + -3.642857143 Combine like terms: 3.563562766 + -3.642857143 = -0.079294377 x = -0.079294377 Simplifying x = -0.079294377Subproblem 2
x + 3.642857143 = -3.563562766 Simplifying x + 3.642857143 = -3.563562766 Reorder the terms: 3.642857143 + x = -3.563562766 Solving 3.642857143 + x = -3.563562766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.642857143' to each side of the equation. 3.642857143 + -3.642857143 + x = -3.563562766 + -3.642857143 Combine like terms: 3.642857143 + -3.642857143 = 0.000000000 0.000000000 + x = -3.563562766 + -3.642857143 x = -3.563562766 + -3.642857143 Combine like terms: -3.563562766 + -3.642857143 = -7.206419909 x = -7.206419909 Simplifying x = -7.206419909Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.079294377, -7.206419909}
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