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Simplifying 3x2 + -39x = 8 Reorder the terms: -39x + 3x2 = 8 Solving -39x + 3x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -39x + 3x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -39x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.666666667 + -13x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + -13x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + -13x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + -13x + x2 = 0 + 2.666666667 -13x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 -13x + x2 = 2.666666667 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 = 2.666666667 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 2.666666667 + 42.25 Combine like terms: 2.666666667 + 42.25 = 44.916666667 42.25 + -13x + x2 = 44.916666667 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 44.916666667 Calculate the square root of the right side: 6.701989754 Break this problem into two subproblems by setting (x + -6.5) equal to 6.701989754 and -6.701989754.Subproblem 1
x + -6.5 = 6.701989754 Simplifying x + -6.5 = 6.701989754 Reorder the terms: -6.5 + x = 6.701989754 Solving -6.5 + x = 6.701989754 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 = 6.701989754 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 6.701989754 + 6.5 x = 6.701989754 + 6.5 Combine like terms: 6.701989754 + 6.5 = 13.201989754 x = 13.201989754 Simplifying x = 13.201989754Subproblem 2
x + -6.5 = -6.701989754 Simplifying x + -6.5 = -6.701989754 Reorder the terms: -6.5 + x = -6.701989754 Solving -6.5 + x = -6.701989754 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 = -6.701989754 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -6.701989754 + 6.5 x = -6.701989754 + 6.5 Combine like terms: -6.701989754 + 6.5 = -0.201989754 x = -0.201989754 Simplifying x = -0.201989754Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.201989754, -0.201989754}
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