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Simplifying 5x + 16 + -5x2 = 0 Reorder the terms: 16 + 5x + -5x2 = 0 Solving 16 + 5x + -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'. -3.2 + -1x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + -1x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + -1x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + -1x + x2 = 0 + 3.2 -1x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 -1x + x2 = 3.2 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 3.2 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 3.2 + 0.25 Combine like terms: 3.2 + 0.25 = 3.45 0.25 + -1x + x2 = 3.45 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 3.45 Calculate the square root of the right side: 1.857417562 Break this problem into two subproblems by setting (x + -0.5) equal to 1.857417562 and -1.857417562.Subproblem 1
x + -0.5 = 1.857417562 Simplifying x + -0.5 = 1.857417562 Reorder the terms: -0.5 + x = 1.857417562 Solving -0.5 + x = 1.857417562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.857417562 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.857417562 + 0.5 x = 1.857417562 + 0.5 Combine like terms: 1.857417562 + 0.5 = 2.357417562 x = 2.357417562 Simplifying x = 2.357417562Subproblem 2
x + -0.5 = -1.857417562 Simplifying x + -0.5 = -1.857417562 Reorder the terms: -0.5 + x = -1.857417562 Solving -0.5 + x = -1.857417562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.857417562 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.857417562 + 0.5 x = -1.857417562 + 0.5 Combine like terms: -1.857417562 + 0.5 = -1.357417562 x = -1.357417562 Simplifying x = -1.357417562Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.357417562, -1.357417562}
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