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Simplifying 9x2 + 23x + -10 = 0 Reorder the terms: -10 + 23x + 9x2 = 0 Solving -10 + 23x + 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 + 2.555555556x + x2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + 2.555555556x + 1.111111111 + x2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + 2.555555556x + x2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + 2.555555556x + x2 = 0 + 1.111111111 2.555555556x + x2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 2.555555556x + x2 = 1.111111111 The x term is 2.555555556x. Take half its coefficient (1.277777778). Square it (1.632716050) and add it to both sides. Add '1.632716050' to each side of the equation. 2.555555556x + 1.632716050 + x2 = 1.111111111 + 1.632716050 Reorder the terms: 1.632716050 + 2.555555556x + x2 = 1.111111111 + 1.632716050 Combine like terms: 1.111111111 + 1.632716050 = 2.743827161 1.632716050 + 2.555555556x + x2 = 2.743827161 Factor a perfect square on the left side: (x + 1.277777778)(x + 1.277777778) = 2.743827161 Calculate the square root of the right side: 1.656450169 Break this problem into two subproblems by setting (x + 1.277777778) equal to 1.656450169 and -1.656450169.Subproblem 1
x + 1.277777778 = 1.656450169 Simplifying x + 1.277777778 = 1.656450169 Reorder the terms: 1.277777778 + x = 1.656450169 Solving 1.277777778 + x = 1.656450169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.277777778' to each side of the equation. 1.277777778 + -1.277777778 + x = 1.656450169 + -1.277777778 Combine like terms: 1.277777778 + -1.277777778 = 0.000000000 0.000000000 + x = 1.656450169 + -1.277777778 x = 1.656450169 + -1.277777778 Combine like terms: 1.656450169 + -1.277777778 = 0.378672391 x = 0.378672391 Simplifying x = 0.378672391Subproblem 2
x + 1.277777778 = -1.656450169 Simplifying x + 1.277777778 = -1.656450169 Reorder the terms: 1.277777778 + x = -1.656450169 Solving 1.277777778 + x = -1.656450169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.277777778' to each side of the equation. 1.277777778 + -1.277777778 + x = -1.656450169 + -1.277777778 Combine like terms: 1.277777778 + -1.277777778 = 0.000000000 0.000000000 + x = -1.656450169 + -1.277777778 x = -1.656450169 + -1.277777778 Combine like terms: -1.656450169 + -1.277777778 = -2.934227947 x = -2.934227947 Simplifying x = -2.934227947Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.378672391, -2.934227947}
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