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Simplifying 4.289x2 + -8.578x + 3.289 = 0 Reorder the terms: 3.289 + -8.578x + 4.289x2 = 0 Solving 3.289 + -8.578x + 4.289x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.289 the coefficient of the squared term: Divide each side by '4.289'. 0.7668454185 + -2x + x2 = 0 Move the constant term to the right: Add '-0.7668454185' to each side of the equation. 0.7668454185 + -2x + -0.7668454185 + x2 = 0 + -0.7668454185 Reorder the terms: 0.7668454185 + -0.7668454185 + -2x + x2 = 0 + -0.7668454185 Combine like terms: 0.7668454185 + -0.7668454185 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + -0.7668454185 -2x + x2 = 0 + -0.7668454185 Combine like terms: 0 + -0.7668454185 = -0.7668454185 -2x + x2 = -0.7668454185 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.7668454185 + 1 Reorder the terms: 1 + -2x + x2 = -0.7668454185 + 1 Combine like terms: -0.7668454185 + 1 = 0.2331545815 1 + -2x + x2 = 0.2331545815 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.2331545815 Calculate the square root of the right side: 0.48286083 Break this problem into two subproblems by setting (x + -1) equal to 0.48286083 and -0.48286083.Subproblem 1
x + -1 = 0.48286083 Simplifying x + -1 = 0.48286083 Reorder the terms: -1 + x = 0.48286083 Solving -1 + x = 0.48286083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.48286083 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.48286083 + 1 x = 0.48286083 + 1 Combine like terms: 0.48286083 + 1 = 1.48286083 x = 1.48286083 Simplifying x = 1.48286083Subproblem 2
x + -1 = -0.48286083 Simplifying x + -1 = -0.48286083 Reorder the terms: -1 + x = -0.48286083 Solving -1 + x = -0.48286083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.48286083 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.48286083 + 1 x = -0.48286083 + 1 Combine like terms: -0.48286083 + 1 = 0.51713917 x = 0.51713917 Simplifying x = 0.51713917Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.48286083, 0.51713917}
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