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Simplifying 49a2 + -70a + -25 = 0 Reorder the terms: -25 + -70a + 49a2 = 0 Solving -25 + -70a + 49a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.5102040816 + -1.428571429a + a2 = 0 Move the constant term to the right: Add '0.5102040816' to each side of the equation. -0.5102040816 + -1.428571429a + 0.5102040816 + a2 = 0 + 0.5102040816 Reorder the terms: -0.5102040816 + 0.5102040816 + -1.428571429a + a2 = 0 + 0.5102040816 Combine like terms: -0.5102040816 + 0.5102040816 = 0.0000000000 0.0000000000 + -1.428571429a + a2 = 0 + 0.5102040816 -1.428571429a + a2 = 0 + 0.5102040816 Combine like terms: 0 + 0.5102040816 = 0.5102040816 -1.428571429a + a2 = 0.5102040816 The a term is -1.428571429a. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429a + 0.5102040819 + a2 = 0.5102040816 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429a + a2 = 0.5102040816 + 0.5102040819 Combine like terms: 0.5102040816 + 0.5102040819 = 1.0204081635 0.5102040819 + -1.428571429a + a2 = 1.0204081635 Factor a perfect square on the left side: (a + -0.7142857145)(a + -0.7142857145) = 1.0204081635 Calculate the square root of the right side: 1.010152545 Break this problem into two subproblems by setting (a + -0.7142857145) equal to 1.010152545 and -1.010152545.Subproblem 1
a + -0.7142857145 = 1.010152545 Simplifying a + -0.7142857145 = 1.010152545 Reorder the terms: -0.7142857145 + a = 1.010152545 Solving -0.7142857145 + a = 1.010152545 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + a = 1.010152545 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + a = 1.010152545 + 0.7142857145 a = 1.010152545 + 0.7142857145 Combine like terms: 1.010152545 + 0.7142857145 = 1.7244382595 a = 1.7244382595 Simplifying a = 1.7244382595Subproblem 2
a + -0.7142857145 = -1.010152545 Simplifying a + -0.7142857145 = -1.010152545 Reorder the terms: -0.7142857145 + a = -1.010152545 Solving -0.7142857145 + a = -1.010152545 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + a = -1.010152545 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + a = -1.010152545 + 0.7142857145 a = -1.010152545 + 0.7142857145 Combine like terms: -1.010152545 + 0.7142857145 = -0.2958668305 a = -0.2958668305 Simplifying a = -0.2958668305Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.7244382595, -0.2958668305}
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