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Simplifying 5x2 + 14x + -120 = 0 Reorder the terms: -120 + 14x + 5x2 = 0 Solving -120 + 14x + 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'. -24 + 2.8x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 2.8x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 2.8x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 2.8x + x2 = 0 + 24 2.8x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 2.8x + x2 = 24 The x term is 2.8x. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8x + 1.96 + x2 = 24 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = 24 + 1.96 Combine like terms: 24 + 1.96 = 25.96 1.96 + 2.8x + x2 = 25.96 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = 25.96 Calculate the square root of the right side: 5.095095681 Break this problem into two subproblems by setting (x + 1.4) equal to 5.095095681 and -5.095095681.Subproblem 1
x + 1.4 = 5.095095681 Simplifying x + 1.4 = 5.095095681 Reorder the terms: 1.4 + x = 5.095095681 Solving 1.4 + x = 5.095095681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = 5.095095681 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 5.095095681 + -1.4 x = 5.095095681 + -1.4 Combine like terms: 5.095095681 + -1.4 = 3.695095681 x = 3.695095681 Simplifying x = 3.695095681Subproblem 2
x + 1.4 = -5.095095681 Simplifying x + 1.4 = -5.095095681 Reorder the terms: 1.4 + x = -5.095095681 Solving 1.4 + x = -5.095095681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = -5.095095681 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -5.095095681 + -1.4 x = -5.095095681 + -1.4 Combine like terms: -5.095095681 + -1.4 = -6.495095681 x = -6.495095681 Simplifying x = -6.495095681Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.695095681, -6.495095681}
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