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Simplifying 4 + 3x + -1 = 9x * x + -6x + 1 Reorder the terms: 4 + -1 + 3x = 9x * x + -6x + 1 Combine like terms: 4 + -1 = 3 3 + 3x = 9x * x + -6x + 1 Multiply x * x 3 + 3x = 9x2 + -6x + 1 Reorder the terms: 3 + 3x = 1 + -6x + 9x2 Solving 3 + 3x = 1 + -6x + 9x2 Solving for variable 'x'. Reorder the terms: 3 + -1 + 3x + 6x + -9x2 = 1 + -6x + 9x2 + -1 + 6x + -9x2 Combine like terms: 3 + -1 = 2 2 + 3x + 6x + -9x2 = 1 + -6x + 9x2 + -1 + 6x + -9x2 Combine like terms: 3x + 6x = 9x 2 + 9x + -9x2 = 1 + -6x + 9x2 + -1 + 6x + -9x2 Reorder the terms: 2 + 9x + -9x2 = 1 + -1 + -6x + 6x + 9x2 + -9x2 Combine like terms: 1 + -1 = 0 2 + 9x + -9x2 = 0 + -6x + 6x + 9x2 + -9x2 2 + 9x + -9x2 = -6x + 6x + 9x2 + -9x2 Combine like terms: -6x + 6x = 0 2 + 9x + -9x2 = 0 + 9x2 + -9x2 2 + 9x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 2 + 9x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.2222222222 + -1x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + -1x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + -1x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + 0.2222222222 -1x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 -1x + x2 = 0.2222222222 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.2222222222 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.2222222222 + 0.25 Combine like terms: 0.2222222222 + 0.25 = 0.4722222222 0.25 + -1x + x2 = 0.4722222222 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.4722222222 Calculate the square root of the right side: 0.687184271 Break this problem into two subproblems by setting (x + -0.5) equal to 0.687184271 and -0.687184271.Subproblem 1
x + -0.5 = 0.687184271 Simplifying x + -0.5 = 0.687184271 Reorder the terms: -0.5 + x = 0.687184271 Solving -0.5 + x = 0.687184271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.687184271 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.687184271 + 0.5 x = 0.687184271 + 0.5 Combine like terms: 0.687184271 + 0.5 = 1.187184271 x = 1.187184271 Simplifying x = 1.187184271Subproblem 2
x + -0.5 = -0.687184271 Simplifying x + -0.5 = -0.687184271 Reorder the terms: -0.5 + x = -0.687184271 Solving -0.5 + x = -0.687184271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.687184271 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.687184271 + 0.5 x = -0.687184271 + 0.5 Combine like terms: -0.687184271 + 0.5 = -0.187184271 x = -0.187184271 Simplifying x = -0.187184271Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.187184271, -0.187184271}
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