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Simplifying -2x2 + 25x + 100 = 0 Reorder the terms: 100 + 25x + -2x2 = 0 Solving 100 + 25x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -50 + -12.5x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -12.5x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -12.5x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -12.5x + x2 = 0 + 50 -12.5x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -12.5x + x2 = 50 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = 50 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = 50 + 39.0625 Combine like terms: 50 + 39.0625 = 89.0625 39.0625 + -12.5x + x2 = 89.0625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 89.0625 Calculate the square root of the right side: 9.437293044 Break this problem into two subproblems by setting (x + -6.25) equal to 9.437293044 and -9.437293044.Subproblem 1
x + -6.25 = 9.437293044 Simplifying x + -6.25 = 9.437293044 Reorder the terms: -6.25 + x = 9.437293044 Solving -6.25 + x = 9.437293044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 9.437293044 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 9.437293044 + 6.25 x = 9.437293044 + 6.25 Combine like terms: 9.437293044 + 6.25 = 15.687293044 x = 15.687293044 Simplifying x = 15.687293044Subproblem 2
x + -6.25 = -9.437293044 Simplifying x + -6.25 = -9.437293044 Reorder the terms: -6.25 + x = -9.437293044 Solving -6.25 + x = -9.437293044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -9.437293044 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -9.437293044 + 6.25 x = -9.437293044 + 6.25 Combine like terms: -9.437293044 + 6.25 = -3.187293044 x = -3.187293044 Simplifying x = -3.187293044Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.687293044, -3.187293044}
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