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Simplifying 13x2 + 125x + 78 = 0 Reorder the terms: 78 + 125x + 13x2 = 0 Solving 78 + 125x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 6 + 9.615384615x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + 9.615384615x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 9.615384615x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 9.615384615x + x2 = 0 + -6 9.615384615x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 9.615384615x + x2 = -6 The x term is 9.615384615x. Take half its coefficient (4.807692308). Square it (23.11390533) and add it to both sides. Add '23.11390533' to each side of the equation. 9.615384615x + 23.11390533 + x2 = -6 + 23.11390533 Reorder the terms: 23.11390533 + 9.615384615x + x2 = -6 + 23.11390533 Combine like terms: -6 + 23.11390533 = 17.11390533 23.11390533 + 9.615384615x + x2 = 17.11390533 Factor a perfect square on the left side: (x + 4.807692308)(x + 4.807692308) = 17.11390533 Calculate the square root of the right side: 4.136895615 Break this problem into two subproblems by setting (x + 4.807692308) equal to 4.136895615 and -4.136895615.Subproblem 1
x + 4.807692308 = 4.136895615 Simplifying x + 4.807692308 = 4.136895615 Reorder the terms: 4.807692308 + x = 4.136895615 Solving 4.807692308 + x = 4.136895615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.807692308' to each side of the equation. 4.807692308 + -4.807692308 + x = 4.136895615 + -4.807692308 Combine like terms: 4.807692308 + -4.807692308 = 0.000000000 0.000000000 + x = 4.136895615 + -4.807692308 x = 4.136895615 + -4.807692308 Combine like terms: 4.136895615 + -4.807692308 = -0.670796693 x = -0.670796693 Simplifying x = -0.670796693Subproblem 2
x + 4.807692308 = -4.136895615 Simplifying x + 4.807692308 = -4.136895615 Reorder the terms: 4.807692308 + x = -4.136895615 Solving 4.807692308 + x = -4.136895615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.807692308' to each side of the equation. 4.807692308 + -4.807692308 + x = -4.136895615 + -4.807692308 Combine like terms: 4.807692308 + -4.807692308 = 0.000000000 0.000000000 + x = -4.136895615 + -4.807692308 x = -4.136895615 + -4.807692308 Combine like terms: -4.136895615 + -4.807692308 = -8.944587923 x = -8.944587923 Simplifying x = -8.944587923Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.670796693, -8.944587923}
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