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Simplifying 49x2 + -70x = -18 Reorder the terms: -70x + 49x2 = -18 Solving -70x + 49x2 = -18 Solving for variable 'x'. Reorder the terms: 18 + -70x + 49x2 = -18 + 18 Combine like terms: -18 + 18 = 0 18 + -70x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.3673469388 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '-0.3673469388' to each side of the equation. 0.3673469388 + -1.428571429x + -0.3673469388 + x2 = 0 + -0.3673469388 Reorder the terms: 0.3673469388 + -0.3673469388 + -1.428571429x + x2 = 0 + -0.3673469388 Combine like terms: 0.3673469388 + -0.3673469388 = 0.0000000000 0.0000000000 + -1.428571429x + x2 = 0 + -0.3673469388 -1.428571429x + x2 = 0 + -0.3673469388 Combine like terms: 0 + -0.3673469388 = -0.3673469388 -1.428571429x + x2 = -0.3673469388 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 = -0.3673469388 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = -0.3673469388 + 0.5102040819 Combine like terms: -0.3673469388 + 0.5102040819 = 0.1428571431 0.5102040819 + -1.428571429x + x2 = 0.1428571431 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 0.1428571431 Calculate the square root of the right side: 0.377964473 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 0.377964473 and -0.377964473.Subproblem 1
x + -0.7142857145 = 0.377964473 Simplifying x + -0.7142857145 = 0.377964473 Reorder the terms: -0.7142857145 + x = 0.377964473 Solving -0.7142857145 + x = 0.377964473 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 = 0.377964473 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 0.377964473 + 0.7142857145 x = 0.377964473 + 0.7142857145 Combine like terms: 0.377964473 + 0.7142857145 = 1.0922501875 x = 1.0922501875 Simplifying x = 1.0922501875Subproblem 2
x + -0.7142857145 = -0.377964473 Simplifying x + -0.7142857145 = -0.377964473 Reorder the terms: -0.7142857145 + x = -0.377964473 Solving -0.7142857145 + x = -0.377964473 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 = -0.377964473 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -0.377964473 + 0.7142857145 x = -0.377964473 + 0.7142857145 Combine like terms: -0.377964473 + 0.7142857145 = 0.3363212415 x = 0.3363212415 Simplifying x = 0.3363212415Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0922501875, 0.3363212415}
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