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Simplifying -0.25x2 + 15x + 300 = 0 Reorder the terms: 300 + 15x + -0.25x2 = 0 Solving 300 + 15x + -0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. -1200 + -60x + x2 = 0 Move the constant term to the right: Add '1200' to each side of the equation. -1200 + -60x + 1200 + x2 = 0 + 1200 Reorder the terms: -1200 + 1200 + -60x + x2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + -60x + x2 = 0 + 1200 -60x + x2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 -60x + x2 = 1200 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = 1200 + 900 Reorder the terms: 900 + -60x + x2 = 1200 + 900 Combine like terms: 1200 + 900 = 2100 900 + -60x + x2 = 2100 Factor a perfect square on the left side: (x + -30)(x + -30) = 2100 Calculate the square root of the right side: 45.82575695 Break this problem into two subproblems by setting (x + -30) equal to 45.82575695 and -45.82575695.Subproblem 1
x + -30 = 45.82575695 Simplifying x + -30 = 45.82575695 Reorder the terms: -30 + x = 45.82575695 Solving -30 + x = 45.82575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 45.82575695 + 30 Combine like terms: -30 + 30 = 0 0 + x = 45.82575695 + 30 x = 45.82575695 + 30 Combine like terms: 45.82575695 + 30 = 75.82575695 x = 75.82575695 Simplifying x = 75.82575695Subproblem 2
x + -30 = -45.82575695 Simplifying x + -30 = -45.82575695 Reorder the terms: -30 + x = -45.82575695 Solving -30 + x = -45.82575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -45.82575695 + 30 Combine like terms: -30 + 30 = 0 0 + x = -45.82575695 + 30 x = -45.82575695 + 30 Combine like terms: -45.82575695 + 30 = -15.82575695 x = -15.82575695 Simplifying x = -15.82575695Solution
The solution to the problem is based on the solutions from the subproblems. x = {75.82575695, -15.82575695}
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