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Simplifying (3x * 3x) + -4x = 10 Reorder the terms for easier multiplication: (3 * 3x * x) + -4x = 10 Multiply 3 * 3 (9x * x) + -4x = 10 Multiply x * x (9x2) + -4x = 10 Reorder the terms: -4x + (9x2) = 10 Solving -4x + (9x2) = 10 Solving for variable 'x'. Reorder the terms: -10 + -4x + (9x2) = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -4x + (9x2) = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.111111111 + -0.4444444444x + x2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + -0.4444444444x + 1.111111111 + x2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + -0.4444444444x + x2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + -0.4444444444x + x2 = 0 + 1.111111111 -0.4444444444x + x2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 -0.4444444444x + x2 = 1.111111111 The x term is -0.4444444444x. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444x + 0.04938271604 + x2 = 1.111111111 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444x + x2 = 1.111111111 + 0.04938271604 Combine like terms: 1.111111111 + 0.04938271604 = 1.16049382704 0.04938271604 + -0.4444444444x + x2 = 1.16049382704 Factor a perfect square on the left side: ((x) + -0.2222222222)((x) + -0.2222222222) = 1.16049382704 Calculate the square root of the right side: 1.07726219 Break this problem into two subproblems by setting ((x) + -0.2222222222) equal to 1.07726219 and -1.07726219.Subproblem 1
(x) + -0.2222222222 = 1.07726219 Simplifying (x) + -0.2222222222 = 1.07726219 x + -0.2222222222 = 1.07726219 Reorder the terms: -0.2222222222 + x = 1.07726219 Solving -0.2222222222 + x = 1.07726219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = 1.07726219 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = 1.07726219 + 0.2222222222 x = 1.07726219 + 0.2222222222 Combine like terms: 1.07726219 + 0.2222222222 = 1.2994844122 x = 1.2994844122 Simplifying x = 1.2994844122Subproblem 2
(x) + -0.2222222222 = -1.07726219 Simplifying (x) + -0.2222222222 = -1.07726219 x + -0.2222222222 = -1.07726219 Reorder the terms: -0.2222222222 + x = -1.07726219 Solving -0.2222222222 + x = -1.07726219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = -1.07726219 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = -1.07726219 + 0.2222222222 x = -1.07726219 + 0.2222222222 Combine like terms: -1.07726219 + 0.2222222222 = -0.8550399678 x = -0.8550399678 Simplifying x = -0.8550399678Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2994844122, -0.8550399678}
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