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Simplifying 3x2 + 2.5x + -9 = 0 Reorder the terms: -9 + 2.5x + 3x2 = 0 Solving -9 + 2.5x + 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'. -3 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 0.8333333333x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 0.8333333333x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 0.8333333333x + x2 = 0 + 3 0.8333333333x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 0.8333333333x + x2 = 3 The x term is 0.8333333333x. Take half its coefficient (0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. 0.8333333333x + 0.1736111111 + x2 = 3 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = 3 + 0.1736111111 Combine like terms: 3 + 0.1736111111 = 3.1736111111 0.1736111111 + 0.8333333333x + x2 = 3.1736111111 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = 3.1736111111 Calculate the square root of the right side: 1.781463194 Break this problem into two subproblems by setting (x + 0.4166666667) equal to 1.781463194 and -1.781463194.Subproblem 1
x + 0.4166666667 = 1.781463194 Simplifying x + 0.4166666667 = 1.781463194 Reorder the terms: 0.4166666667 + x = 1.781463194 Solving 0.4166666667 + x = 1.781463194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = 1.781463194 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = 1.781463194 + -0.4166666667 x = 1.781463194 + -0.4166666667 Combine like terms: 1.781463194 + -0.4166666667 = 1.3647965273 x = 1.3647965273 Simplifying x = 1.3647965273Subproblem 2
x + 0.4166666667 = -1.781463194 Simplifying x + 0.4166666667 = -1.781463194 Reorder the terms: 0.4166666667 + x = -1.781463194 Solving 0.4166666667 + x = -1.781463194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = -1.781463194 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = -1.781463194 + -0.4166666667 x = -1.781463194 + -0.4166666667 Combine like terms: -1.781463194 + -0.4166666667 = -2.1981298607 x = -2.1981298607 Simplifying x = -2.1981298607Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3647965273, -2.1981298607}
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