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Simplifying 4x2 + 9x = 1 Reorder the terms: 9x + 4x2 = 1 Solving 9x + 4x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 9x + 4x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + 2.25x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 2.25x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 2.25x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 2.25x + x2 = 0 + 0.25 2.25x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 2.25x + x2 = 0.25 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 = 0.25 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 0.25 + 1.265625 Combine like terms: 0.25 + 1.265625 = 1.515625 1.265625 + 2.25x + x2 = 1.515625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 1.515625 Calculate the square root of the right side: 1.231107225 Break this problem into two subproblems by setting (x + 1.125) equal to 1.231107225 and -1.231107225.Subproblem 1
x + 1.125 = 1.231107225 Simplifying x + 1.125 = 1.231107225 Reorder the terms: 1.125 + x = 1.231107225 Solving 1.125 + x = 1.231107225 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 = 1.231107225 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 1.231107225 + -1.125 x = 1.231107225 + -1.125 Combine like terms: 1.231107225 + -1.125 = 0.106107225 x = 0.106107225 Simplifying x = 0.106107225Subproblem 2
x + 1.125 = -1.231107225 Simplifying x + 1.125 = -1.231107225 Reorder the terms: 1.125 + x = -1.231107225 Solving 1.125 + x = -1.231107225 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 = -1.231107225 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -1.231107225 + -1.125 x = -1.231107225 + -1.125 Combine like terms: -1.231107225 + -1.125 = -2.356107225 x = -2.356107225 Simplifying x = -2.356107225Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.106107225, -2.356107225}
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