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Simplifying 5x2 + 6x + -128 = 0 Reorder the terms: -128 + 6x + 5x2 = 0 Solving -128 + 6x + 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'. -25.6 + 1.2x + x2 = 0 Move the constant term to the right: Add '25.6' to each side of the equation. -25.6 + 1.2x + 25.6 + x2 = 0 + 25.6 Reorder the terms: -25.6 + 25.6 + 1.2x + x2 = 0 + 25.6 Combine like terms: -25.6 + 25.6 = 0.0 0.0 + 1.2x + x2 = 0 + 25.6 1.2x + x2 = 0 + 25.6 Combine like terms: 0 + 25.6 = 25.6 1.2x + x2 = 25.6 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 25.6 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 25.6 + 0.36 Combine like terms: 25.6 + 0.36 = 25.96 0.36 + 1.2x + x2 = 25.96 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 25.96 Calculate the square root of the right side: 5.095095681 Break this problem into two subproblems by setting (x + 0.6) equal to 5.095095681 and -5.095095681.Subproblem 1
x + 0.6 = 5.095095681 Simplifying x + 0.6 = 5.095095681 Reorder the terms: 0.6 + x = 5.095095681 Solving 0.6 + x = 5.095095681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 5.095095681 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 5.095095681 + -0.6 x = 5.095095681 + -0.6 Combine like terms: 5.095095681 + -0.6 = 4.495095681 x = 4.495095681 Simplifying x = 4.495095681Subproblem 2
x + 0.6 = -5.095095681 Simplifying x + 0.6 = -5.095095681 Reorder the terms: 0.6 + x = -5.095095681 Solving 0.6 + x = -5.095095681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -5.095095681 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -5.095095681 + -0.6 x = -5.095095681 + -0.6 Combine like terms: -5.095095681 + -0.6 = -5.695095681 x = -5.695095681 Simplifying x = -5.695095681Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.495095681, -5.695095681}
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