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Simplifying 7x2 + 40x + 43 = 0 Reorder the terms: 43 + 40x + 7x2 = 0 Solving 43 + 40x + 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'. 6.142857143 + 5.714285714x + x2 = 0 Move the constant term to the right: Add '-6.142857143' to each side of the equation. 6.142857143 + 5.714285714x + -6.142857143 + x2 = 0 + -6.142857143 Reorder the terms: 6.142857143 + -6.142857143 + 5.714285714x + x2 = 0 + -6.142857143 Combine like terms: 6.142857143 + -6.142857143 = 0.000000000 0.000000000 + 5.714285714x + x2 = 0 + -6.142857143 5.714285714x + x2 = 0 + -6.142857143 Combine like terms: 0 + -6.142857143 = -6.142857143 5.714285714x + x2 = -6.142857143 The x term is 5.714285714x. Take half its coefficient (2.857142857). Square it (8.163265305) and add it to both sides. Add '8.163265305' to each side of the equation. 5.714285714x + 8.163265305 + x2 = -6.142857143 + 8.163265305 Reorder the terms: 8.163265305 + 5.714285714x + x2 = -6.142857143 + 8.163265305 Combine like terms: -6.142857143 + 8.163265305 = 2.020408162 8.163265305 + 5.714285714x + x2 = 2.020408162 Factor a perfect square on the left side: (x + 2.857142857)(x + 2.857142857) = 2.020408162 Calculate the square root of the right side: 1.421410624 Break this problem into two subproblems by setting (x + 2.857142857) equal to 1.421410624 and -1.421410624.Subproblem 1
x + 2.857142857 = 1.421410624 Simplifying x + 2.857142857 = 1.421410624 Reorder the terms: 2.857142857 + x = 1.421410624 Solving 2.857142857 + x = 1.421410624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.857142857' to each side of the equation. 2.857142857 + -2.857142857 + x = 1.421410624 + -2.857142857 Combine like terms: 2.857142857 + -2.857142857 = 0.000000000 0.000000000 + x = 1.421410624 + -2.857142857 x = 1.421410624 + -2.857142857 Combine like terms: 1.421410624 + -2.857142857 = -1.435732233 x = -1.435732233 Simplifying x = -1.435732233Subproblem 2
x + 2.857142857 = -1.421410624 Simplifying x + 2.857142857 = -1.421410624 Reorder the terms: 2.857142857 + x = -1.421410624 Solving 2.857142857 + x = -1.421410624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.857142857' to each side of the equation. 2.857142857 + -2.857142857 + x = -1.421410624 + -2.857142857 Combine like terms: 2.857142857 + -2.857142857 = 0.000000000 0.000000000 + x = -1.421410624 + -2.857142857 x = -1.421410624 + -2.857142857 Combine like terms: -1.421410624 + -2.857142857 = -4.278553481 x = -4.278553481 Simplifying x = -4.278553481Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.435732233, -4.278553481}
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