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Simplifying 7x2 + 77x + x + 11 = 171 Reorder the terms: 11 + 77x + x + 7x2 = 171 Combine like terms: 77x + x = 78x 11 + 78x + 7x2 = 171 Solving 11 + 78x + 7x2 = 171 Solving for variable 'x'. Reorder the terms: 11 + -171 + 78x + 7x2 = 171 + -171 Combine like terms: 11 + -171 = -160 -160 + 78x + 7x2 = 171 + -171 Combine like terms: 171 + -171 = 0 -160 + 78x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -22.85714286 + 11.14285714x + x2 = 0 Move the constant term to the right: Add '22.85714286' to each side of the equation. -22.85714286 + 11.14285714x + 22.85714286 + x2 = 0 + 22.85714286 Reorder the terms: -22.85714286 + 22.85714286 + 11.14285714x + x2 = 0 + 22.85714286 Combine like terms: -22.85714286 + 22.85714286 = 0.00000000 0.00000000 + 11.14285714x + x2 = 0 + 22.85714286 11.14285714x + x2 = 0 + 22.85714286 Combine like terms: 0 + 22.85714286 = 22.85714286 11.14285714x + x2 = 22.85714286 The x term is 11.14285714x. Take half its coefficient (5.57142857). Square it (31.04081631) and add it to both sides. Add '31.04081631' to each side of the equation. 11.14285714x + 31.04081631 + x2 = 22.85714286 + 31.04081631 Reorder the terms: 31.04081631 + 11.14285714x + x2 = 22.85714286 + 31.04081631 Combine like terms: 22.85714286 + 31.04081631 = 53.89795917 31.04081631 + 11.14285714x + x2 = 53.89795917 Factor a perfect square on the left side: (x + 5.57142857)(x + 5.57142857) = 53.89795917 Calculate the square root of the right side: 7.341522946 Break this problem into two subproblems by setting (x + 5.57142857) equal to 7.341522946 and -7.341522946.Subproblem 1
x + 5.57142857 = 7.341522946 Simplifying x + 5.57142857 = 7.341522946 Reorder the terms: 5.57142857 + x = 7.341522946 Solving 5.57142857 + x = 7.341522946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.57142857' to each side of the equation. 5.57142857 + -5.57142857 + x = 7.341522946 + -5.57142857 Combine like terms: 5.57142857 + -5.57142857 = 0.00000000 0.00000000 + x = 7.341522946 + -5.57142857 x = 7.341522946 + -5.57142857 Combine like terms: 7.341522946 + -5.57142857 = 1.770094376 x = 1.770094376 Simplifying x = 1.770094376Subproblem 2
x + 5.57142857 = -7.341522946 Simplifying x + 5.57142857 = -7.341522946 Reorder the terms: 5.57142857 + x = -7.341522946 Solving 5.57142857 + x = -7.341522946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.57142857' to each side of the equation. 5.57142857 + -5.57142857 + x = -7.341522946 + -5.57142857 Combine like terms: 5.57142857 + -5.57142857 = 0.00000000 0.00000000 + x = -7.341522946 + -5.57142857 x = -7.341522946 + -5.57142857 Combine like terms: -7.341522946 + -5.57142857 = -12.912951516 x = -12.912951516 Simplifying x = -12.912951516Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.770094376, -12.912951516}
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