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Simplifying 0.6x2 + 2x + -9 = 0 Reorder the terms: -9 + 2x + 0.6x2 = 0 Solving -9 + 2x + 0.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. -15 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 3.333333333x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 3.333333333x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 3.333333333x + x2 = 0 + 15 3.333333333x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 3.333333333x + x2 = 15 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 = 15 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 15 + 2.777777779 Combine like terms: 15 + 2.777777779 = 17.777777779 2.777777779 + 3.333333333x + x2 = 17.777777779 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 17.777777779 Calculate the square root of the right side: 4.216370214 Break this problem into two subproblems by setting (x + 1.666666667) equal to 4.216370214 and -4.216370214.Subproblem 1
x + 1.666666667 = 4.216370214 Simplifying x + 1.666666667 = 4.216370214 Reorder the terms: 1.666666667 + x = 4.216370214 Solving 1.666666667 + x = 4.216370214 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 = 4.216370214 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 4.216370214 + -1.666666667 x = 4.216370214 + -1.666666667 Combine like terms: 4.216370214 + -1.666666667 = 2.549703547 x = 2.549703547 Simplifying x = 2.549703547Subproblem 2
x + 1.666666667 = -4.216370214 Simplifying x + 1.666666667 = -4.216370214 Reorder the terms: 1.666666667 + x = -4.216370214 Solving 1.666666667 + x = -4.216370214 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 = -4.216370214 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -4.216370214 + -1.666666667 x = -4.216370214 + -1.666666667 Combine like terms: -4.216370214 + -1.666666667 = -5.883036881 x = -5.883036881 Simplifying x = -5.883036881Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.549703547, -5.883036881}
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