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Simplifying 2x2 + 10x + -2475 = 0 Reorder the terms: -2475 + 10x + 2x2 = 0 Solving -2475 + 10x + 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'. -1237.5 + 5x + x2 = 0 Move the constant term to the right: Add '1237.5' to each side of the equation. -1237.5 + 5x + 1237.5 + x2 = 0 + 1237.5 Reorder the terms: -1237.5 + 1237.5 + 5x + x2 = 0 + 1237.5 Combine like terms: -1237.5 + 1237.5 = 0.0 0.0 + 5x + x2 = 0 + 1237.5 5x + x2 = 0 + 1237.5 Combine like terms: 0 + 1237.5 = 1237.5 5x + x2 = 1237.5 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 = 1237.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 1237.5 + 6.25 Combine like terms: 1237.5 + 6.25 = 1243.75 6.25 + 5x + x2 = 1243.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 1243.75 Calculate the square root of the right side: 35.266839949 Break this problem into two subproblems by setting (x + 2.5) equal to 35.266839949 and -35.266839949.Subproblem 1
x + 2.5 = 35.266839949 Simplifying x + 2.5 = 35.266839949 Reorder the terms: 2.5 + x = 35.266839949 Solving 2.5 + x = 35.266839949 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 = 35.266839949 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 35.266839949 + -2.5 x = 35.266839949 + -2.5 Combine like terms: 35.266839949 + -2.5 = 32.766839949 x = 32.766839949 Simplifying x = 32.766839949Subproblem 2
x + 2.5 = -35.266839949 Simplifying x + 2.5 = -35.266839949 Reorder the terms: 2.5 + x = -35.266839949 Solving 2.5 + x = -35.266839949 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 = -35.266839949 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -35.266839949 + -2.5 x = -35.266839949 + -2.5 Combine like terms: -35.266839949 + -2.5 = -37.766839949 x = -37.766839949 Simplifying x = -37.766839949Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.766839949, -37.766839949}
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