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Simplifying 2x2 + 28x + 75 = 0 Reorder the terms: 75 + 28x + 2x2 = 0 Solving 75 + 28x + 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 + 14x + x2 = 0 Move the constant term to the right: Add '-37.5' to each side of the equation. 37.5 + 14x + -37.5 + x2 = 0 + -37.5 Reorder the terms: 37.5 + -37.5 + 14x + x2 = 0 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + 14x + x2 = 0 + -37.5 14x + x2 = 0 + -37.5 Combine like terms: 0 + -37.5 = -37.5 14x + x2 = -37.5 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = -37.5 + 49 Reorder the terms: 49 + 14x + x2 = -37.5 + 49 Combine like terms: -37.5 + 49 = 11.5 49 + 14x + x2 = 11.5 Factor a perfect square on the left side: (x + 7)(x + 7) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (x + 7) equal to 3.391164992 and -3.391164992.Subproblem 1
x + 7 = 3.391164992 Simplifying x + 7 = 3.391164992 Reorder the terms: 7 + x = 3.391164992 Solving 7 + x = 3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 3.391164992 + -7 Combine like terms: 7 + -7 = 0 0 + x = 3.391164992 + -7 x = 3.391164992 + -7 Combine like terms: 3.391164992 + -7 = -3.608835008 x = -3.608835008 Simplifying x = -3.608835008Subproblem 2
x + 7 = -3.391164992 Simplifying x + 7 = -3.391164992 Reorder the terms: 7 + x = -3.391164992 Solving 7 + x = -3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -3.391164992 + -7 Combine like terms: 7 + -7 = 0 0 + x = -3.391164992 + -7 x = -3.391164992 + -7 Combine like terms: -3.391164992 + -7 = -10.391164992 x = -10.391164992 Simplifying x = -10.391164992Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.608835008, -10.391164992}
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