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Simplifying 7x2 + 11x + -165 = 0 Reorder the terms: -165 + 11x + 7x2 = 0 Solving -165 + 11x + 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'. -23.57142857 + 1.571428571x + x2 = 0 Move the constant term to the right: Add '23.57142857' to each side of the equation. -23.57142857 + 1.571428571x + 23.57142857 + x2 = 0 + 23.57142857 Reorder the terms: -23.57142857 + 23.57142857 + 1.571428571x + x2 = 0 + 23.57142857 Combine like terms: -23.57142857 + 23.57142857 = 0.00000000 0.00000000 + 1.571428571x + x2 = 0 + 23.57142857 1.571428571x + x2 = 0 + 23.57142857 Combine like terms: 0 + 23.57142857 = 23.57142857 1.571428571x + x2 = 23.57142857 The x term is 1.571428571x. Take half its coefficient (0.7857142855). Square it (0.6173469384) and add it to both sides. Add '0.6173469384' to each side of the equation. 1.571428571x + 0.6173469384 + x2 = 23.57142857 + 0.6173469384 Reorder the terms: 0.6173469384 + 1.571428571x + x2 = 23.57142857 + 0.6173469384 Combine like terms: 23.57142857 + 0.6173469384 = 24.1887755084 0.6173469384 + 1.571428571x + x2 = 24.1887755084 Factor a perfect square on the left side: (x + 0.7857142855)(x + 0.7857142855) = 24.1887755084 Calculate the square root of the right side: 4.918208567 Break this problem into two subproblems by setting (x + 0.7857142855) equal to 4.918208567 and -4.918208567.Subproblem 1
x + 0.7857142855 = 4.918208567 Simplifying x + 0.7857142855 = 4.918208567 Reorder the terms: 0.7857142855 + x = 4.918208567 Solving 0.7857142855 + x = 4.918208567 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + x = 4.918208567 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = 4.918208567 + -0.7857142855 x = 4.918208567 + -0.7857142855 Combine like terms: 4.918208567 + -0.7857142855 = 4.1324942815 x = 4.1324942815 Simplifying x = 4.1324942815Subproblem 2
x + 0.7857142855 = -4.918208567 Simplifying x + 0.7857142855 = -4.918208567 Reorder the terms: 0.7857142855 + x = -4.918208567 Solving 0.7857142855 + x = -4.918208567 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + x = -4.918208567 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = -4.918208567 + -0.7857142855 x = -4.918208567 + -0.7857142855 Combine like terms: -4.918208567 + -0.7857142855 = -5.7039228525 x = -5.7039228525 Simplifying x = -5.7039228525Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.1324942815, -5.7039228525}
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