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Simplifying 169x2 + 78x + -56 = 0 Reorder the terms: -56 + 78x + 169x2 = 0 Solving -56 + 78x + 169x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 169 the coefficient of the squared term: Divide each side by '169'. -0.3313609467 + 0.4615384615x + x2 = 0 Move the constant term to the right: Add '0.3313609467' to each side of the equation. -0.3313609467 + 0.4615384615x + 0.3313609467 + x2 = 0 + 0.3313609467 Reorder the terms: -0.3313609467 + 0.3313609467 + 0.4615384615x + x2 = 0 + 0.3313609467 Combine like terms: -0.3313609467 + 0.3313609467 = 0.0000000000 0.0000000000 + 0.4615384615x + x2 = 0 + 0.3313609467 0.4615384615x + x2 = 0 + 0.3313609467 Combine like terms: 0 + 0.3313609467 = 0.3313609467 0.4615384615x + x2 = 0.3313609467 The x term is 0.4615384615x. Take half its coefficient (0.2307692308). Square it (0.05325443788) and add it to both sides. Add '0.05325443788' to each side of the equation. 0.4615384615x + 0.05325443788 + x2 = 0.3313609467 + 0.05325443788 Reorder the terms: 0.05325443788 + 0.4615384615x + x2 = 0.3313609467 + 0.05325443788 Combine like terms: 0.3313609467 + 0.05325443788 = 0.38461538458 0.05325443788 + 0.4615384615x + x2 = 0.38461538458 Factor a perfect square on the left side: (x + 0.2307692308)(x + 0.2307692308) = 0.38461538458 Calculate the square root of the right side: 0.620173673 Break this problem into two subproblems by setting (x + 0.2307692308) equal to 0.620173673 and -0.620173673.Subproblem 1
x + 0.2307692308 = 0.620173673 Simplifying x + 0.2307692308 = 0.620173673 Reorder the terms: 0.2307692308 + x = 0.620173673 Solving 0.2307692308 + x = 0.620173673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2307692308' to each side of the equation. 0.2307692308 + -0.2307692308 + x = 0.620173673 + -0.2307692308 Combine like terms: 0.2307692308 + -0.2307692308 = 0.0000000000 0.0000000000 + x = 0.620173673 + -0.2307692308 x = 0.620173673 + -0.2307692308 Combine like terms: 0.620173673 + -0.2307692308 = 0.3894044422 x = 0.3894044422 Simplifying x = 0.3894044422Subproblem 2
x + 0.2307692308 = -0.620173673 Simplifying x + 0.2307692308 = -0.620173673 Reorder the terms: 0.2307692308 + x = -0.620173673 Solving 0.2307692308 + x = -0.620173673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2307692308' to each side of the equation. 0.2307692308 + -0.2307692308 + x = -0.620173673 + -0.2307692308 Combine like terms: 0.2307692308 + -0.2307692308 = 0.0000000000 0.0000000000 + x = -0.620173673 + -0.2307692308 x = -0.620173673 + -0.2307692308 Combine like terms: -0.620173673 + -0.2307692308 = -0.8509429038 x = -0.8509429038 Simplifying x = -0.8509429038Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3894044422, -0.8509429038}
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