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Simplifying 4.905x2 + 2.551x = 0.332 Reorder the terms: 2.551x + 4.905x2 = 0.332 Solving 2.551x + 4.905x2 = 0.332 Solving for variable 'x'. Reorder the terms: -0.332 + 2.551x + 4.905x2 = 0.332 + -0.332 Combine like terms: 0.332 + -0.332 = 0.000 -0.332 + 2.551x + 4.905x2 = 0.000 Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -0.06768603466 + 0.5200815494x + x2 = 0 Move the constant term to the right: Add '0.06768603466' to each side of the equation. -0.06768603466 + 0.5200815494x + 0.06768603466 + x2 = 0 + 0.06768603466 Reorder the terms: -0.06768603466 + 0.06768603466 + 0.5200815494x + x2 = 0 + 0.06768603466 Combine like terms: -0.06768603466 + 0.06768603466 = 0.00000000000 0.00000000000 + 0.5200815494x + x2 = 0 + 0.06768603466 0.5200815494x + x2 = 0 + 0.06768603466 Combine like terms: 0 + 0.06768603466 = 0.06768603466 0.5200815494x + x2 = 0.06768603466 The x term is 0.5200815494x. Take half its coefficient (0.2600407747). Square it (0.06762120451) and add it to both sides. Add '0.06762120451' to each side of the equation. 0.5200815494x + 0.06762120451 + x2 = 0.06768603466 + 0.06762120451 Reorder the terms: 0.06762120451 + 0.5200815494x + x2 = 0.06768603466 + 0.06762120451 Combine like terms: 0.06768603466 + 0.06762120451 = 0.13530723917 0.06762120451 + 0.5200815494x + x2 = 0.13530723917 Factor a perfect square on the left side: (x + 0.2600407747)(x + 0.2600407747) = 0.13530723917 Calculate the square root of the right side: 0.367841323 Break this problem into two subproblems by setting (x + 0.2600407747) equal to 0.367841323 and -0.367841323.Subproblem 1
x + 0.2600407747 = 0.367841323 Simplifying x + 0.2600407747 = 0.367841323 Reorder the terms: 0.2600407747 + x = 0.367841323 Solving 0.2600407747 + x = 0.367841323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2600407747' to each side of the equation. 0.2600407747 + -0.2600407747 + x = 0.367841323 + -0.2600407747 Combine like terms: 0.2600407747 + -0.2600407747 = 0.0000000000 0.0000000000 + x = 0.367841323 + -0.2600407747 x = 0.367841323 + -0.2600407747 Combine like terms: 0.367841323 + -0.2600407747 = 0.1078005483 x = 0.1078005483 Simplifying x = 0.1078005483Subproblem 2
x + 0.2600407747 = -0.367841323 Simplifying x + 0.2600407747 = -0.367841323 Reorder the terms: 0.2600407747 + x = -0.367841323 Solving 0.2600407747 + x = -0.367841323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2600407747' to each side of the equation. 0.2600407747 + -0.2600407747 + x = -0.367841323 + -0.2600407747 Combine like terms: 0.2600407747 + -0.2600407747 = 0.0000000000 0.0000000000 + x = -0.367841323 + -0.2600407747 x = -0.367841323 + -0.2600407747 Combine like terms: -0.367841323 + -0.2600407747 = -0.6278820977 x = -0.6278820977 Simplifying x = -0.6278820977Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1078005483, -0.6278820977}
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