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Simplifying 2970x(198x + -178) + -7921 = 0 Reorder the terms: 2970x(-178 + 198x) + -7921 = 0 (-178 * 2970x + 198x * 2970x) + -7921 = 0 (-528660x + 588060x2) + -7921 = 0 Reorder the terms: -7921 + -528660x + 588060x2 = 0 Solving -7921 + -528660x + 588060x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 588060 the coefficient of the squared term: Divide each side by '588060'. -0.01346971397 + -0.898989899x + x2 = 0.0 Move the constant term to the right: Add '0.01346971397' to each side of the equation. -0.01346971397 + -0.898989899x + 0.01346971397 + x2 = 0.0 + 0.01346971397 Reorder the terms: -0.01346971397 + 0.01346971397 + -0.898989899x + x2 = 0.0 + 0.01346971397 Combine like terms: -0.01346971397 + 0.01346971397 = 0.00000000000 0.00000000000 + -0.898989899x + x2 = 0.0 + 0.01346971397 -0.898989899x + x2 = 0.0 + 0.01346971397 Combine like terms: 0.0 + 0.01346971397 = 0.01346971397 -0.898989899x + x2 = 0.01346971397 The x term is -0.898989899x. Take half its coefficient (-0.4494949495). Square it (0.2020457096) and add it to both sides. Add '0.2020457096' to each side of the equation. -0.898989899x + 0.2020457096 + x2 = 0.01346971397 + 0.2020457096 Reorder the terms: 0.2020457096 + -0.898989899x + x2 = 0.01346971397 + 0.2020457096 Combine like terms: 0.01346971397 + 0.2020457096 = 0.21551542357 0.2020457096 + -0.898989899x + x2 = 0.21551542357 Factor a perfect square on the left side: (x + -0.4494949495)(x + -0.4494949495) = 0.21551542357 Calculate the square root of the right side: 0.464236388 Break this problem into two subproblems by setting (x + -0.4494949495) equal to 0.464236388 and -0.464236388.Subproblem 1
x + -0.4494949495 = 0.464236388 Simplifying x + -0.4494949495 = 0.464236388 Reorder the terms: -0.4494949495 + x = 0.464236388 Solving -0.4494949495 + x = 0.464236388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4494949495' to each side of the equation. -0.4494949495 + 0.4494949495 + x = 0.464236388 + 0.4494949495 Combine like terms: -0.4494949495 + 0.4494949495 = 0.0000000000 0.0000000000 + x = 0.464236388 + 0.4494949495 x = 0.464236388 + 0.4494949495 Combine like terms: 0.464236388 + 0.4494949495 = 0.9137313375 x = 0.9137313375 Simplifying x = 0.9137313375Subproblem 2
x + -0.4494949495 = -0.464236388 Simplifying x + -0.4494949495 = -0.464236388 Reorder the terms: -0.4494949495 + x = -0.464236388 Solving -0.4494949495 + x = -0.464236388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4494949495' to each side of the equation. -0.4494949495 + 0.4494949495 + x = -0.464236388 + 0.4494949495 Combine like terms: -0.4494949495 + 0.4494949495 = 0.0000000000 0.0000000000 + x = -0.464236388 + 0.4494949495 x = -0.464236388 + 0.4494949495 Combine like terms: -0.464236388 + 0.4494949495 = -0.0147414385 x = -0.0147414385 Simplifying x = -0.0147414385Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9137313375, -0.0147414385}
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