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Simplifying 0.5x2 + 14x + -8500 = 0 Reorder the terms: -8500 + 14x + 0.5x2 = 0 Solving -8500 + 14x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -17000 + 28x + x2 = 0 Move the constant term to the right: Add '17000' to each side of the equation. -17000 + 28x + 17000 + x2 = 0 + 17000 Reorder the terms: -17000 + 17000 + 28x + x2 = 0 + 17000 Combine like terms: -17000 + 17000 = 0 0 + 28x + x2 = 0 + 17000 28x + x2 = 0 + 17000 Combine like terms: 0 + 17000 = 17000 28x + x2 = 17000 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = 17000 + 196 Reorder the terms: 196 + 28x + x2 = 17000 + 196 Combine like terms: 17000 + 196 = 17196 196 + 28x + x2 = 17196 Factor a perfect square on the left side: (x + 14)(x + 14) = 17196 Calculate the square root of the right side: 131.133519742 Break this problem into two subproblems by setting (x + 14) equal to 131.133519742 and -131.133519742.Subproblem 1
x + 14 = 131.133519742 Simplifying x + 14 = 131.133519742 Reorder the terms: 14 + x = 131.133519742 Solving 14 + x = 131.133519742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 131.133519742 + -14 Combine like terms: 14 + -14 = 0 0 + x = 131.133519742 + -14 x = 131.133519742 + -14 Combine like terms: 131.133519742 + -14 = 117.133519742 x = 117.133519742 Simplifying x = 117.133519742Subproblem 2
x + 14 = -131.133519742 Simplifying x + 14 = -131.133519742 Reorder the terms: 14 + x = -131.133519742 Solving 14 + x = -131.133519742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -131.133519742 + -14 Combine like terms: 14 + -14 = 0 0 + x = -131.133519742 + -14 x = -131.133519742 + -14 Combine like terms: -131.133519742 + -14 = -145.133519742 x = -145.133519742 Simplifying x = -145.133519742Solution
The solution to the problem is based on the solutions from the subproblems. x = {117.133519742, -145.133519742}
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