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Simplifying 25 = -0.25(x2 + -100x) Reorder the terms: 25 = -0.25(-100x + x2) 25 = (-100x * -0.25 + x2 * -0.25) 25 = (25x + -0.25x2) Solving 25 = 25x + -0.25x2 Solving for variable 'x'. Reorder the terms: 25 + -25x + 0.25x2 = 25x + -25x + -0.25x2 + 0.25x2 Combine like terms: 25x + -25x = 0 25 + -25x + 0.25x2 = 0 + -0.25x2 + 0.25x2 25 + -25x + 0.25x2 = -0.25x2 + 0.25x2 Combine like terms: -0.25x2 + 0.25x2 = 0.00 25 + -25x + 0.25x2 = 0.00 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 100 + -100x + x2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + -100x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -100x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -100x + x2 = 0 + -100 -100x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -100x + x2 = -100 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -100 + 2500 Reorder the terms: 2500 + -100x + x2 = -100 + 2500 Combine like terms: -100 + 2500 = 2400 2500 + -100x + x2 = 2400 Factor a perfect square on the left side: (x + -50)(x + -50) = 2400 Calculate the square root of the right side: 48.989794856 Break this problem into two subproblems by setting (x + -50) equal to 48.989794856 and -48.989794856.Subproblem 1
x + -50 = 48.989794856 Simplifying x + -50 = 48.989794856 Reorder the terms: -50 + x = 48.989794856 Solving -50 + x = 48.989794856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 48.989794856 + 50 Combine like terms: -50 + 50 = 0 0 + x = 48.989794856 + 50 x = 48.989794856 + 50 Combine like terms: 48.989794856 + 50 = 98.989794856 x = 98.989794856 Simplifying x = 98.989794856Subproblem 2
x + -50 = -48.989794856 Simplifying x + -50 = -48.989794856 Reorder the terms: -50 + x = -48.989794856 Solving -50 + x = -48.989794856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -48.989794856 + 50 Combine like terms: -50 + 50 = 0 0 + x = -48.989794856 + 50 x = -48.989794856 + 50 Combine like terms: -48.989794856 + 50 = 1.010205144 x = 1.010205144 Simplifying x = 1.010205144Solution
The solution to the problem is based on the solutions from the subproblems. x = {98.989794856, 1.010205144}
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