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Simplifying 5x(2x + 1) + (5 + -9) = 0 Reorder the terms: 5x(1 + 2x) + (5 + -9) = 0 (1 * 5x + 2x * 5x) + (5 + -9) = 0 (5x + 10x2) + (5 + -9) = 0 Combine like terms: 5 + -9 = -4 5x + 10x2 + (-4) = 0 5x + 10x2 + -4 = 0 Reorder the terms: -4 + 5x + 10x2 = 0 Solving -4 + 5x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.4 + 0.5x + x2 = 0.0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 0.5x + 0.4 + x2 = 0.0 + 0.4 Reorder the terms: -0.4 + 0.4 + 0.5x + x2 = 0.0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 0.5x + x2 = 0.0 + 0.4 0.5x + x2 = 0.0 + 0.4 Combine like terms: 0.0 + 0.4 = 0.4 0.5x + x2 = 0.4 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 = 0.4 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.4 + 0.0625 Combine like terms: 0.4 + 0.0625 = 0.4625 0.0625 + 0.5x + x2 = 0.4625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.4625 Calculate the square root of the right side: 0.680073525 Break this problem into two subproblems by setting (x + 0.25) equal to 0.680073525 and -0.680073525.Subproblem 1
x + 0.25 = 0.680073525 Simplifying x + 0.25 = 0.680073525 Reorder the terms: 0.25 + x = 0.680073525 Solving 0.25 + x = 0.680073525 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 = 0.680073525 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.680073525 + -0.25 x = 0.680073525 + -0.25 Combine like terms: 0.680073525 + -0.25 = 0.430073525 x = 0.430073525 Simplifying x = 0.430073525Subproblem 2
x + 0.25 = -0.680073525 Simplifying x + 0.25 = -0.680073525 Reorder the terms: 0.25 + x = -0.680073525 Solving 0.25 + x = -0.680073525 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 = -0.680073525 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.680073525 + -0.25 x = -0.680073525 + -0.25 Combine like terms: -0.680073525 + -0.25 = -0.930073525 x = -0.930073525 Simplifying x = -0.930073525Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.430073525, -0.930073525}
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