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Simplifying 7.06(x)(x) + -4.85x + 0.5 = 0 Multiply x * x 7.06x2 + -4.85x + 0.5 = 0 Reorder the terms: 0.5 + -4.85x + 7.06x2 = 0 Solving 0.5 + -4.85x + 7.06x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7.06 the coefficient of the squared term: Divide each side by '7.06'. 0.07082152975 + -0.6869688385x + x2 = 0 Move the constant term to the right: Add '-0.07082152975' to each side of the equation. 0.07082152975 + -0.6869688385x + -0.07082152975 + x2 = 0 + -0.07082152975 Reorder the terms: 0.07082152975 + -0.07082152975 + -0.6869688385x + x2 = 0 + -0.07082152975 Combine like terms: 0.07082152975 + -0.07082152975 = 0.00000000000 0.00000000000 + -0.6869688385x + x2 = 0 + -0.07082152975 -0.6869688385x + x2 = 0 + -0.07082152975 Combine like terms: 0 + -0.07082152975 = -0.07082152975 -0.6869688385x + x2 = -0.07082152975 The x term is -0.6869688385x. Take half its coefficient (-0.3434844193). Square it (0.1179815463) and add it to both sides. Add '0.1179815463' to each side of the equation. -0.6869688385x + 0.1179815463 + x2 = -0.07082152975 + 0.1179815463 Reorder the terms: 0.1179815463 + -0.6869688385x + x2 = -0.07082152975 + 0.1179815463 Combine like terms: -0.07082152975 + 0.1179815463 = 0.04716001655 0.1179815463 + -0.6869688385x + x2 = 0.04716001655 Factor a perfect square on the left side: (x + -0.3434844193)(x + -0.3434844193) = 0.04716001655 Calculate the square root of the right side: 0.217163571 Break this problem into two subproblems by setting (x + -0.3434844193) equal to 0.217163571 and -0.217163571.Subproblem 1
x + -0.3434844193 = 0.217163571 Simplifying x + -0.3434844193 = 0.217163571 Reorder the terms: -0.3434844193 + x = 0.217163571 Solving -0.3434844193 + x = 0.217163571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3434844193' to each side of the equation. -0.3434844193 + 0.3434844193 + x = 0.217163571 + 0.3434844193 Combine like terms: -0.3434844193 + 0.3434844193 = 0.0000000000 0.0000000000 + x = 0.217163571 + 0.3434844193 x = 0.217163571 + 0.3434844193 Combine like terms: 0.217163571 + 0.3434844193 = 0.5606479903 x = 0.5606479903 Simplifying x = 0.5606479903Subproblem 2
x + -0.3434844193 = -0.217163571 Simplifying x + -0.3434844193 = -0.217163571 Reorder the terms: -0.3434844193 + x = -0.217163571 Solving -0.3434844193 + x = -0.217163571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3434844193' to each side of the equation. -0.3434844193 + 0.3434844193 + x = -0.217163571 + 0.3434844193 Combine like terms: -0.3434844193 + 0.3434844193 = 0.0000000000 0.0000000000 + x = -0.217163571 + 0.3434844193 x = -0.217163571 + 0.3434844193 Combine like terms: -0.217163571 + 0.3434844193 = 0.1263208483 x = 0.1263208483 Simplifying x = 0.1263208483Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5606479903, 0.1263208483}
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