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Simplifying 0.638x2 + 6.671x + 627.619 = 720000 Reorder the terms: 627.619 + 6.671x + 0.638x2 = 720000 Solving 627.619 + 6.671x + 0.638x2 = 720000 Solving for variable 'x'. Reorder the terms: 627.619 + -720000 + 6.671x + 0.638x2 = 720000 + -720000 Combine like terms: 627.619 + -720000 = -719372.381 -719372.381 + 6.671x + 0.638x2 = 720000 + -720000 Combine like terms: 720000 + -720000 = 0 -719372.381 + 6.671x + 0.638x2 = 0 Begin completing the square. Divide all terms by 0.638 the coefficient of the squared term: Divide each side by '0.638'. -1127542.917 + 10.45611285x + x2 = 0 Move the constant term to the right: Add '1127542.917' to each side of the equation. -1127542.917 + 10.45611285x + 1127542.917 + x2 = 0 + 1127542.917 Reorder the terms: -1127542.917 + 1127542.917 + 10.45611285x + x2 = 0 + 1127542.917 Combine like terms: -1127542.917 + 1127542.917 = 0.000 0.000 + 10.45611285x + x2 = 0 + 1127542.917 10.45611285x + x2 = 0 + 1127542.917 Combine like terms: 0 + 1127542.917 = 1127542.917 10.45611285x + x2 = 1127542.917 The x term is 10.45611285x. Take half its coefficient (5.228056425). Square it (27.33257398) and add it to both sides. Add '27.33257398' to each side of the equation. 10.45611285x + 27.33257398 + x2 = 1127542.917 + 27.33257398 Reorder the terms: 27.33257398 + 10.45611285x + x2 = 1127542.917 + 27.33257398 Combine like terms: 1127542.917 + 27.33257398 = 1127570.24957398 27.33257398 + 10.45611285x + x2 = 1127570.24957398 Factor a perfect square on the left side: (x + 5.228056425)(x + 5.228056425) = 1127570.24957398 Calculate the square root of the right side: 1061.871107797 Break this problem into two subproblems by setting (x + 5.228056425) equal to 1061.871107797 and -1061.871107797.Subproblem 1
x + 5.228056425 = 1061.871107797 Simplifying x + 5.228056425 = 1061.871107797 Reorder the terms: 5.228056425 + x = 1061.871107797 Solving 5.228056425 + x = 1061.871107797 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.228056425' to each side of the equation. 5.228056425 + -5.228056425 + x = 1061.871107797 + -5.228056425 Combine like terms: 5.228056425 + -5.228056425 = 0.000000000 0.000000000 + x = 1061.871107797 + -5.228056425 x = 1061.871107797 + -5.228056425 Combine like terms: 1061.871107797 + -5.228056425 = 1056.643051372 x = 1056.643051372 Simplifying x = 1056.643051372Subproblem 2
x + 5.228056425 = -1061.871107797 Simplifying x + 5.228056425 = -1061.871107797 Reorder the terms: 5.228056425 + x = -1061.871107797 Solving 5.228056425 + x = -1061.871107797 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.228056425' to each side of the equation. 5.228056425 + -5.228056425 + x = -1061.871107797 + -5.228056425 Combine like terms: 5.228056425 + -5.228056425 = 0.000000000 0.000000000 + x = -1061.871107797 + -5.228056425 x = -1061.871107797 + -5.228056425 Combine like terms: -1061.871107797 + -5.228056425 = -1067.099164222 x = -1067.099164222 Simplifying x = -1067.099164222Solution
The solution to the problem is based on the solutions from the subproblems. x = {1056.643051372, -1067.099164222}
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