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Simplifying 100 = 5x + x2 Solving 100 = 5x + x2 Solving for variable 'x'. Reorder the terms: 100 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 100 + -5x + -1x2 = 0 + x2 + -1x2 100 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 100 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -100 + 5x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 5x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 5x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 5x + x2 = 0 + 100 5x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 5x + x2 = 100 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 100 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 100 + 6.25 Combine like terms: 100 + 6.25 = 106.25 6.25 + 5x + x2 = 106.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (x + 2.5) equal to 10.307764064 and -10.307764064.Subproblem 1
x + 2.5 = 10.307764064 Simplifying x + 2.5 = 10.307764064 Reorder the terms: 2.5 + x = 10.307764064 Solving 2.5 + x = 10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 10.307764064 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 10.307764064 + -2.5 x = 10.307764064 + -2.5 Combine like terms: 10.307764064 + -2.5 = 7.807764064 x = 7.807764064 Simplifying x = 7.807764064Subproblem 2
x + 2.5 = -10.307764064 Simplifying x + 2.5 = -10.307764064 Reorder the terms: 2.5 + x = -10.307764064 Solving 2.5 + x = -10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -10.307764064 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -10.307764064 + -2.5 x = -10.307764064 + -2.5 Combine like terms: -10.307764064 + -2.5 = -12.807764064 x = -12.807764064 Simplifying x = -12.807764064Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.807764064, -12.807764064}
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