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Simplifying 9x2 + 39x + -10 = 0 Reorder the terms: -10 + 39x + 9x2 = 0 Solving -10 + 39x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.111111111 + 4.333333333x + x2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + 4.333333333x + 1.111111111 + x2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + 4.333333333x + x2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + 4.333333333x + x2 = 0 + 1.111111111 4.333333333x + x2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 4.333333333x + x2 = 1.111111111 The x term is 4.333333333x. Take half its coefficient (2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. 4.333333333x + 4.694444446 + x2 = 1.111111111 + 4.694444446 Reorder the terms: 4.694444446 + 4.333333333x + x2 = 1.111111111 + 4.694444446 Combine like terms: 1.111111111 + 4.694444446 = 5.805555557 4.694444446 + 4.333333333x + x2 = 5.805555557 Factor a perfect square on the left side: (x + 2.166666667)(x + 2.166666667) = 5.805555557 Calculate the square root of the right side: 2.409472049 Break this problem into two subproblems by setting (x + 2.166666667) equal to 2.409472049 and -2.409472049.Subproblem 1
x + 2.166666667 = 2.409472049 Simplifying x + 2.166666667 = 2.409472049 Reorder the terms: 2.166666667 + x = 2.409472049 Solving 2.166666667 + x = 2.409472049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = 2.409472049 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = 2.409472049 + -2.166666667 x = 2.409472049 + -2.166666667 Combine like terms: 2.409472049 + -2.166666667 = 0.242805382 x = 0.242805382 Simplifying x = 0.242805382Subproblem 2
x + 2.166666667 = -2.409472049 Simplifying x + 2.166666667 = -2.409472049 Reorder the terms: 2.166666667 + x = -2.409472049 Solving 2.166666667 + x = -2.409472049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = -2.409472049 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = -2.409472049 + -2.166666667 x = -2.409472049 + -2.166666667 Combine like terms: -2.409472049 + -2.166666667 = -4.576138716 x = -4.576138716 Simplifying x = -4.576138716Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.242805382, -4.576138716}
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