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Simplifying 2x2 + 7x + -625 = 0 Reorder the terms: -625 + 7x + 2x2 = 0 Solving -625 + 7x + 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'. -312.5 + 3.5x + x2 = 0 Move the constant term to the right: Add '312.5' to each side of the equation. -312.5 + 3.5x + 312.5 + x2 = 0 + 312.5 Reorder the terms: -312.5 + 312.5 + 3.5x + x2 = 0 + 312.5 Combine like terms: -312.5 + 312.5 = 0.0 0.0 + 3.5x + x2 = 0 + 312.5 3.5x + x2 = 0 + 312.5 Combine like terms: 0 + 312.5 = 312.5 3.5x + x2 = 312.5 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 312.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 312.5 + 3.0625 Combine like terms: 312.5 + 3.0625 = 315.5625 3.0625 + 3.5x + x2 = 315.5625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 315.5625 Calculate the square root of the right side: 17.764078923 Break this problem into two subproblems by setting (x + 1.75) equal to 17.764078923 and -17.764078923.Subproblem 1
x + 1.75 = 17.764078923 Simplifying x + 1.75 = 17.764078923 Reorder the terms: 1.75 + x = 17.764078923 Solving 1.75 + x = 17.764078923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 17.764078923 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 17.764078923 + -1.75 x = 17.764078923 + -1.75 Combine like terms: 17.764078923 + -1.75 = 16.014078923 x = 16.014078923 Simplifying x = 16.014078923Subproblem 2
x + 1.75 = -17.764078923 Simplifying x + 1.75 = -17.764078923 Reorder the terms: 1.75 + x = -17.764078923 Solving 1.75 + x = -17.764078923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -17.764078923 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -17.764078923 + -1.75 x = -17.764078923 + -1.75 Combine like terms: -17.764078923 + -1.75 = -19.514078923 x = -19.514078923 Simplifying x = -19.514078923Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.014078923, -19.514078923}
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