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Simplifying 3.1x2 + -14x + 5 = 0 Reorder the terms: 5 + -14x + 3.1x2 = 0 Solving 5 + -14x + 3.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.1 the coefficient of the squared term: Divide each side by '3.1'. 1.612903226 + -4.516129032x + x2 = 0 Move the constant term to the right: Add '-1.612903226' to each side of the equation. 1.612903226 + -4.516129032x + -1.612903226 + x2 = 0 + -1.612903226 Reorder the terms: 1.612903226 + -1.612903226 + -4.516129032x + x2 = 0 + -1.612903226 Combine like terms: 1.612903226 + -1.612903226 = 0.000000000 0.000000000 + -4.516129032x + x2 = 0 + -1.612903226 -4.516129032x + x2 = 0 + -1.612903226 Combine like terms: 0 + -1.612903226 = -1.612903226 -4.516129032x + x2 = -1.612903226 The x term is -4.516129032x. Take half its coefficient (-2.258064516). Square it (5.098855358) and add it to both sides. Add '5.098855358' to each side of the equation. -4.516129032x + 5.098855358 + x2 = -1.612903226 + 5.098855358 Reorder the terms: 5.098855358 + -4.516129032x + x2 = -1.612903226 + 5.098855358 Combine like terms: -1.612903226 + 5.098855358 = 3.485952132 5.098855358 + -4.516129032x + x2 = 3.485952132 Factor a perfect square on the left side: (x + -2.258064516)(x + -2.258064516) = 3.485952132 Calculate the square root of the right side: 1.867070468 Break this problem into two subproblems by setting (x + -2.258064516) equal to 1.867070468 and -1.867070468.Subproblem 1
x + -2.258064516 = 1.867070468 Simplifying x + -2.258064516 = 1.867070468 Reorder the terms: -2.258064516 + x = 1.867070468 Solving -2.258064516 + x = 1.867070468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.258064516' to each side of the equation. -2.258064516 + 2.258064516 + x = 1.867070468 + 2.258064516 Combine like terms: -2.258064516 + 2.258064516 = 0.000000000 0.000000000 + x = 1.867070468 + 2.258064516 x = 1.867070468 + 2.258064516 Combine like terms: 1.867070468 + 2.258064516 = 4.125134984 x = 4.125134984 Simplifying x = 4.125134984Subproblem 2
x + -2.258064516 = -1.867070468 Simplifying x + -2.258064516 = -1.867070468 Reorder the terms: -2.258064516 + x = -1.867070468 Solving -2.258064516 + x = -1.867070468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.258064516' to each side of the equation. -2.258064516 + 2.258064516 + x = -1.867070468 + 2.258064516 Combine like terms: -2.258064516 + 2.258064516 = 0.000000000 0.000000000 + x = -1.867070468 + 2.258064516 x = -1.867070468 + 2.258064516 Combine like terms: -1.867070468 + 2.258064516 = 0.390994048 x = 0.390994048 Simplifying x = 0.390994048Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.125134984, 0.390994048}
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