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Simplifying 14.52 = -0.5x2 + 5x + 15 Reorder the terms: 14.52 = 15 + 5x + -0.5x2 Solving 14.52 = 15 + 5x + -0.5x2 Solving for variable 'x'. Combine like terms: 14.52 + -15 = -0.48 -0.48 + -5x + 0.5x2 = 15 + 5x + -0.5x2 + -15 + -5x + 0.5x2 Reorder the terms: -0.48 + -5x + 0.5x2 = 15 + -15 + 5x + -5x + -0.5x2 + 0.5x2 Combine like terms: 15 + -15 = 0 -0.48 + -5x + 0.5x2 = 0 + 5x + -5x + -0.5x2 + 0.5x2 -0.48 + -5x + 0.5x2 = 5x + -5x + -0.5x2 + 0.5x2 Combine like terms: 5x + -5x = 0 -0.48 + -5x + 0.5x2 = 0 + -0.5x2 + 0.5x2 -0.48 + -5x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 -0.48 + -5x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -0.96 + -10x + x2 = 0 Move the constant term to the right: Add '0.96' to each side of the equation. -0.96 + -10x + 0.96 + x2 = 0 + 0.96 Reorder the terms: -0.96 + 0.96 + -10x + x2 = 0 + 0.96 Combine like terms: -0.96 + 0.96 = 0.00 0.00 + -10x + x2 = 0 + 0.96 -10x + x2 = 0 + 0.96 Combine like terms: 0 + 0.96 = 0.96 -10x + x2 = 0.96 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 0.96 + 25 Reorder the terms: 25 + -10x + x2 = 0.96 + 25 Combine like terms: 0.96 + 25 = 25.96 25 + -10x + x2 = 25.96 Factor a perfect square on the left side: (x + -5)(x + -5) = 25.96 Calculate the square root of the right side: 5.095095681 Break this problem into two subproblems by setting (x + -5) equal to 5.095095681 and -5.095095681.Subproblem 1
x + -5 = 5.095095681 Simplifying x + -5 = 5.095095681 Reorder the terms: -5 + x = 5.095095681 Solving -5 + x = 5.095095681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.095095681 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.095095681 + 5 x = 5.095095681 + 5 Combine like terms: 5.095095681 + 5 = 10.095095681 x = 10.095095681 Simplifying x = 10.095095681Subproblem 2
x + -5 = -5.095095681 Simplifying x + -5 = -5.095095681 Reorder the terms: -5 + x = -5.095095681 Solving -5 + x = -5.095095681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.095095681 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.095095681 + 5 x = -5.095095681 + 5 Combine like terms: -5.095095681 + 5 = -0.095095681 x = -0.095095681 Simplifying x = -0.095095681Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.095095681, -0.095095681}
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