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Simplifying 2x2 + 10x + -75 = 0 Reorder the terms: -75 + 10x + 2x2 = 0 Solving -75 + 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'. -37.5 + 5x + x2 = 0 Move the constant term to the right: Add '37.5' to each side of the equation. -37.5 + 5x + 37.5 + x2 = 0 + 37.5 Reorder the terms: -37.5 + 37.5 + 5x + x2 = 0 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + 5x + x2 = 0 + 37.5 5x + x2 = 0 + 37.5 Combine like terms: 0 + 37.5 = 37.5 5x + x2 = 37.5 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 = 37.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 37.5 + 6.25 Combine like terms: 37.5 + 6.25 = 43.75 6.25 + 5x + x2 = 43.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 43.75 Calculate the square root of the right side: 6.614378278 Break this problem into two subproblems by setting (x + 2.5) equal to 6.614378278 and -6.614378278.Subproblem 1
x + 2.5 = 6.614378278 Simplifying x + 2.5 = 6.614378278 Reorder the terms: 2.5 + x = 6.614378278 Solving 2.5 + x = 6.614378278 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 = 6.614378278 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 6.614378278 + -2.5 x = 6.614378278 + -2.5 Combine like terms: 6.614378278 + -2.5 = 4.114378278 x = 4.114378278 Simplifying x = 4.114378278Subproblem 2
x + 2.5 = -6.614378278 Simplifying x + 2.5 = -6.614378278 Reorder the terms: 2.5 + x = -6.614378278 Solving 2.5 + x = -6.614378278 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 = -6.614378278 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -6.614378278 + -2.5 x = -6.614378278 + -2.5 Combine like terms: -6.614378278 + -2.5 = -9.114378278 x = -9.114378278 Simplifying x = -9.114378278Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.114378278, -9.114378278}
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