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Simplifying 4x2 + 11x = 9x + 19 Reorder the terms: 11x + 4x2 = 9x + 19 Reorder the terms: 11x + 4x2 = 19 + 9x Solving 11x + 4x2 = 19 + 9x Solving for variable 'x'. Reorder the terms: -19 + 11x + -9x + 4x2 = 19 + 9x + -19 + -9x Combine like terms: 11x + -9x = 2x -19 + 2x + 4x2 = 19 + 9x + -19 + -9x Reorder the terms: -19 + 2x + 4x2 = 19 + -19 + 9x + -9x Combine like terms: 19 + -19 = 0 -19 + 2x + 4x2 = 0 + 9x + -9x -19 + 2x + 4x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -19 + 2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.75 + 0.5x + x2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + 0.5x + 4.75 + x2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + 0.5x + x2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + 0.5x + x2 = 0 + 4.75 0.5x + x2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 0.5x + x2 = 4.75 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 4.75 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 4.75 + 0.0625 Combine like terms: 4.75 + 0.0625 = 4.8125 0.0625 + 0.5x + x2 = 4.8125 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 4.8125 Calculate the square root of the right side: 2.193741097 Break this problem into two subproblems by setting (x + 0.25) equal to 2.193741097 and -2.193741097.Subproblem 1
x + 0.25 = 2.193741097 Simplifying x + 0.25 = 2.193741097 Reorder the terms: 0.25 + x = 2.193741097 Solving 0.25 + x = 2.193741097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 2.193741097 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 2.193741097 + -0.25 x = 2.193741097 + -0.25 Combine like terms: 2.193741097 + -0.25 = 1.943741097 x = 1.943741097 Simplifying x = 1.943741097Subproblem 2
x + 0.25 = -2.193741097 Simplifying x + 0.25 = -2.193741097 Reorder the terms: 0.25 + x = -2.193741097 Solving 0.25 + x = -2.193741097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -2.193741097 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -2.193741097 + -0.25 x = -2.193741097 + -0.25 Combine like terms: -2.193741097 + -0.25 = -2.443741097 x = -2.443741097 Simplifying x = -2.443741097Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.943741097, -2.443741097}
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