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Simplifying 4.9x2 + -340x + 1734 = 0 Reorder the terms: 1734 + -340x + 4.9x2 = 0 Solving 1734 + -340x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 353.877551 + -69.3877551x + x2 = 0 Move the constant term to the right: Add '-353.877551' to each side of the equation. 353.877551 + -69.3877551x + -353.877551 + x2 = 0 + -353.877551 Reorder the terms: 353.877551 + -353.877551 + -69.3877551x + x2 = 0 + -353.877551 Combine like terms: 353.877551 + -353.877551 = 0.000000 0.000000 + -69.3877551x + x2 = 0 + -353.877551 -69.3877551x + x2 = 0 + -353.877551 Combine like terms: 0 + -353.877551 = -353.877551 -69.3877551x + x2 = -353.877551 The x term is -69.3877551x. Take half its coefficient (-34.69387755). Square it (1203.665139) and add it to both sides. Add '1203.665139' to each side of the equation. -69.3877551x + 1203.665139 + x2 = -353.877551 + 1203.665139 Reorder the terms: 1203.665139 + -69.3877551x + x2 = -353.877551 + 1203.665139 Combine like terms: -353.877551 + 1203.665139 = 849.787588 1203.665139 + -69.3877551x + x2 = 849.787588 Factor a perfect square on the left side: (x + -34.69387755)(x + -34.69387755) = 849.787588 Calculate the square root of the right side: 29.151116411 Break this problem into two subproblems by setting (x + -34.69387755) equal to 29.151116411 and -29.151116411.Subproblem 1
x + -34.69387755 = 29.151116411 Simplifying x + -34.69387755 = 29.151116411 Reorder the terms: -34.69387755 + x = 29.151116411 Solving -34.69387755 + x = 29.151116411 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '34.69387755' to each side of the equation. -34.69387755 + 34.69387755 + x = 29.151116411 + 34.69387755 Combine like terms: -34.69387755 + 34.69387755 = 0.00000000 0.00000000 + x = 29.151116411 + 34.69387755 x = 29.151116411 + 34.69387755 Combine like terms: 29.151116411 + 34.69387755 = 63.844993961 x = 63.844993961 Simplifying x = 63.844993961Subproblem 2
x + -34.69387755 = -29.151116411 Simplifying x + -34.69387755 = -29.151116411 Reorder the terms: -34.69387755 + x = -29.151116411 Solving -34.69387755 + x = -29.151116411 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '34.69387755' to each side of the equation. -34.69387755 + 34.69387755 + x = -29.151116411 + 34.69387755 Combine like terms: -34.69387755 + 34.69387755 = 0.00000000 0.00000000 + x = -29.151116411 + 34.69387755 x = -29.151116411 + 34.69387755 Combine like terms: -29.151116411 + 34.69387755 = 5.542761139 x = 5.542761139 Simplifying x = 5.542761139Solution
The solution to the problem is based on the solutions from the subproblems. x = {63.844993961, 5.542761139}
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