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Simplifying 5x2 + 56x + 27 = 0 Reorder the terms: 27 + 56x + 5x2 = 0 Solving 27 + 56x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 5.4 + 11.2x + x2 = 0 Move the constant term to the right: Add '-5.4' to each side of the equation. 5.4 + 11.2x + -5.4 + x2 = 0 + -5.4 Reorder the terms: 5.4 + -5.4 + 11.2x + x2 = 0 + -5.4 Combine like terms: 5.4 + -5.4 = 0.0 0.0 + 11.2x + x2 = 0 + -5.4 11.2x + x2 = 0 + -5.4 Combine like terms: 0 + -5.4 = -5.4 11.2x + x2 = -5.4 The x term is 11.2x. Take half its coefficient (5.6). Square it (31.36) and add it to both sides. Add '31.36' to each side of the equation. 11.2x + 31.36 + x2 = -5.4 + 31.36 Reorder the terms: 31.36 + 11.2x + x2 = -5.4 + 31.36 Combine like terms: -5.4 + 31.36 = 25.96 31.36 + 11.2x + x2 = 25.96 Factor a perfect square on the left side: (x + 5.6)(x + 5.6) = 25.96 Calculate the square root of the right side: 5.095095681 Break this problem into two subproblems by setting (x + 5.6) equal to 5.095095681 and -5.095095681.Subproblem 1
x + 5.6 = 5.095095681 Simplifying x + 5.6 = 5.095095681 Reorder the terms: 5.6 + x = 5.095095681 Solving 5.6 + x = 5.095095681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.6' to each side of the equation. 5.6 + -5.6 + x = 5.095095681 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + x = 5.095095681 + -5.6 x = 5.095095681 + -5.6 Combine like terms: 5.095095681 + -5.6 = -0.504904319 x = -0.504904319 Simplifying x = -0.504904319Subproblem 2
x + 5.6 = -5.095095681 Simplifying x + 5.6 = -5.095095681 Reorder the terms: 5.6 + x = -5.095095681 Solving 5.6 + x = -5.095095681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.6' to each side of the equation. 5.6 + -5.6 + x = -5.095095681 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + x = -5.095095681 + -5.6 x = -5.095095681 + -5.6 Combine like terms: -5.095095681 + -5.6 = -10.695095681 x = -10.695095681 Simplifying x = -10.695095681Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.504904319, -10.695095681}
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