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Simplifying 4x2 + 1 = 9x + -2 Reorder the terms: 1 + 4x2 = 9x + -2 Reorder the terms: 1 + 4x2 = -2 + 9x Solving 1 + 4x2 = -2 + 9x Solving for variable 'x'. Reorder the terms: 1 + 2 + -9x + 4x2 = -2 + 9x + 2 + -9x Combine like terms: 1 + 2 = 3 3 + -9x + 4x2 = -2 + 9x + 2 + -9x Reorder the terms: 3 + -9x + 4x2 = -2 + 2 + 9x + -9x Combine like terms: -2 + 2 = 0 3 + -9x + 4x2 = 0 + 9x + -9x 3 + -9x + 4x2 = 9x + -9x Combine like terms: 9x + -9x = 0 3 + -9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + -2.25x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -2.25x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -2.25x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -2.25x + x2 = 0 + -0.75 -2.25x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -2.25x + x2 = -0.75 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = -0.75 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = -0.75 + 1.265625 Combine like terms: -0.75 + 1.265625 = 0.515625 1.265625 + -2.25x + x2 = 0.515625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 0.515625 Calculate the square root of the right side: 0.718070331 Break this problem into two subproblems by setting (x + -1.125) equal to 0.718070331 and -0.718070331.Subproblem 1
x + -1.125 = 0.718070331 Simplifying x + -1.125 = 0.718070331 Reorder the terms: -1.125 + x = 0.718070331 Solving -1.125 + x = 0.718070331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 0.718070331 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 0.718070331 + 1.125 x = 0.718070331 + 1.125 Combine like terms: 0.718070331 + 1.125 = 1.843070331 x = 1.843070331 Simplifying x = 1.843070331Subproblem 2
x + -1.125 = -0.718070331 Simplifying x + -1.125 = -0.718070331 Reorder the terms: -1.125 + x = -0.718070331 Solving -1.125 + x = -0.718070331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -0.718070331 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -0.718070331 + 1.125 x = -0.718070331 + 1.125 Combine like terms: -0.718070331 + 1.125 = 0.406929669 x = 0.406929669 Simplifying x = 0.406929669Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.843070331, 0.406929669}
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