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Simplifying 3x2 + 10x + -39 = 0 Reorder the terms: -39 + 10x + 3x2 = 0 Solving -39 + 10x + 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'. -13 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 3.333333333x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 3.333333333x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 3.333333333x + x2 = 0 + 13 3.333333333x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 3.333333333x + x2 = 13 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = 13 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 13 + 2.777777779 Combine like terms: 13 + 2.777777779 = 15.777777779 2.777777779 + 3.333333333x + x2 = 15.777777779 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 15.777777779 Calculate the square root of the right side: 3.972125096 Break this problem into two subproblems by setting (x + 1.666666667) equal to 3.972125096 and -3.972125096.Subproblem 1
x + 1.666666667 = 3.972125096 Simplifying x + 1.666666667 = 3.972125096 Reorder the terms: 1.666666667 + x = 3.972125096 Solving 1.666666667 + x = 3.972125096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 3.972125096 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 3.972125096 + -1.666666667 x = 3.972125096 + -1.666666667 Combine like terms: 3.972125096 + -1.666666667 = 2.305458429 x = 2.305458429 Simplifying x = 2.305458429Subproblem 2
x + 1.666666667 = -3.972125096 Simplifying x + 1.666666667 = -3.972125096 Reorder the terms: 1.666666667 + x = -3.972125096 Solving 1.666666667 + x = -3.972125096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -3.972125096 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -3.972125096 + -1.666666667 x = -3.972125096 + -1.666666667 Combine like terms: -3.972125096 + -1.666666667 = -5.638791763 x = -5.638791763 Simplifying x = -5.638791763Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.305458429, -5.638791763}
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