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Simplifying 7x2 + 23x + 4 = 0 Reorder the terms: 4 + 23x + 7x2 = 0 Solving 4 + 23x + 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 + 3.285714286x + x2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + 3.285714286x + -0.5714285714 + x2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + 3.285714286x + x2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + 3.285714286x + x2 = 0 + -0.5714285714 3.285714286x + x2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 3.285714286x + x2 = -0.5714285714 The x term is 3.285714286x. Take half its coefficient (1.642857143). Square it (2.698979592) and add it to both sides. Add '2.698979592' to each side of the equation. 3.285714286x + 2.698979592 + x2 = -0.5714285714 + 2.698979592 Reorder the terms: 2.698979592 + 3.285714286x + x2 = -0.5714285714 + 2.698979592 Combine like terms: -0.5714285714 + 2.698979592 = 2.1275510206 2.698979592 + 3.285714286x + x2 = 2.1275510206 Factor a perfect square on the left side: (x + 1.642857143)(x + 1.642857143) = 2.1275510206 Calculate the square root of the right side: 1.458612704 Break this problem into two subproblems by setting (x + 1.642857143) equal to 1.458612704 and -1.458612704.Subproblem 1
x + 1.642857143 = 1.458612704 Simplifying x + 1.642857143 = 1.458612704 Reorder the terms: 1.642857143 + x = 1.458612704 Solving 1.642857143 + x = 1.458612704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.642857143' to each side of the equation. 1.642857143 + -1.642857143 + x = 1.458612704 + -1.642857143 Combine like terms: 1.642857143 + -1.642857143 = 0.000000000 0.000000000 + x = 1.458612704 + -1.642857143 x = 1.458612704 + -1.642857143 Combine like terms: 1.458612704 + -1.642857143 = -0.184244439 x = -0.184244439 Simplifying x = -0.184244439Subproblem 2
x + 1.642857143 = -1.458612704 Simplifying x + 1.642857143 = -1.458612704 Reorder the terms: 1.642857143 + x = -1.458612704 Solving 1.642857143 + x = -1.458612704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.642857143' to each side of the equation. 1.642857143 + -1.642857143 + x = -1.458612704 + -1.642857143 Combine like terms: 1.642857143 + -1.642857143 = 0.000000000 0.000000000 + x = -1.458612704 + -1.642857143 x = -1.458612704 + -1.642857143 Combine like terms: -1.458612704 + -1.642857143 = -3.101469847 x = -3.101469847 Simplifying x = -3.101469847Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.184244439, -3.101469847}
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