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Simplifying 3x2 + -39x + 7 = 0 Reorder the terms: 7 + -39x + 3x2 = 0 Solving 7 + -39x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + -13x + x2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -13x + -2.333333333 + x2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -13x + x2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -13x + x2 = 0 + -2.333333333 -13x + x2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -13x + x2 = -2.333333333 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -2.333333333 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -2.333333333 + 42.25 Combine like terms: -2.333333333 + 42.25 = 39.916666667 42.25 + -13x + x2 = 39.916666667 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 39.916666667 Calculate the square root of the right side: 6.317963807 Break this problem into two subproblems by setting (x + -6.5) equal to 6.317963807 and -6.317963807.Subproblem 1
x + -6.5 = 6.317963807 Simplifying x + -6.5 = 6.317963807 Reorder the terms: -6.5 + x = 6.317963807 Solving -6.5 + x = 6.317963807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 6.317963807 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 6.317963807 + 6.5 x = 6.317963807 + 6.5 Combine like terms: 6.317963807 + 6.5 = 12.817963807 x = 12.817963807 Simplifying x = 12.817963807Subproblem 2
x + -6.5 = -6.317963807 Simplifying x + -6.5 = -6.317963807 Reorder the terms: -6.5 + x = -6.317963807 Solving -6.5 + x = -6.317963807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -6.317963807 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -6.317963807 + 6.5 x = -6.317963807 + 6.5 Combine like terms: -6.317963807 + 6.5 = 0.182036193 x = 0.182036193 Simplifying x = 0.182036193Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.817963807, 0.182036193}
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