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Simplifying 49x2 + 70x = 25 Reorder the terms: 70x + 49x2 = 25 Solving 70x + 49x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + 70x + 49x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 70x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.5102040816 + 1.428571429x + x2 = 0 Move the constant term to the right: Add '0.5102040816' to each side of the equation. -0.5102040816 + 1.428571429x + 0.5102040816 + x2 = 0 + 0.5102040816 Reorder the terms: -0.5102040816 + 0.5102040816 + 1.428571429x + x2 = 0 + 0.5102040816 Combine like terms: -0.5102040816 + 0.5102040816 = 0.0000000000 0.0000000000 + 1.428571429x + x2 = 0 + 0.5102040816 1.428571429x + x2 = 0 + 0.5102040816 Combine like terms: 0 + 0.5102040816 = 0.5102040816 1.428571429x + x2 = 0.5102040816 The x term is 1.428571429x. 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. 1.428571429x + 0.5102040819 + x2 = 0.5102040816 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429x + x2 = 0.5102040816 + 0.5102040819 Combine like terms: 0.5102040816 + 0.5102040819 = 1.0204081635 0.5102040819 + 1.428571429x + x2 = 1.0204081635 Factor a perfect square on the left side: (x + 0.7142857145)(x + 0.7142857145) = 1.0204081635 Calculate the square root of the right side: 1.010152545 Break this problem into two subproblems by setting (x + 0.7142857145) equal to 1.010152545 and -1.010152545.Subproblem 1
x + 0.7142857145 = 1.010152545 Simplifying x + 0.7142857145 = 1.010152545 Reorder the terms: 0.7142857145 + x = 1.010152545 Solving 0.7142857145 + x = 1.010152545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = 1.010152545 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 1.010152545 + -0.7142857145 x = 1.010152545 + -0.7142857145 Combine like terms: 1.010152545 + -0.7142857145 = 0.2958668305 x = 0.2958668305 Simplifying x = 0.2958668305Subproblem 2
x + 0.7142857145 = -1.010152545 Simplifying x + 0.7142857145 = -1.010152545 Reorder the terms: 0.7142857145 + x = -1.010152545 Solving 0.7142857145 + x = -1.010152545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = -1.010152545 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -1.010152545 + -0.7142857145 x = -1.010152545 + -0.7142857145 Combine like terms: -1.010152545 + -0.7142857145 = -1.7244382595 x = -1.7244382595 Simplifying x = -1.7244382595Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2958668305, -1.7244382595}
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