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Simplifying 2x2 + -5x + -30 = 5 Reorder the terms: -30 + -5x + 2x2 = 5 Solving -30 + -5x + 2x2 = 5 Solving for variable 'x'. Reorder the terms: -30 + -5 + -5x + 2x2 = 5 + -5 Combine like terms: -30 + -5 = -35 -35 + -5x + 2x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -35 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -2.5x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -2.5x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -2.5x + x2 = 0 + 17.5 -2.5x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -2.5x + x2 = 17.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 17.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 17.5 + 1.5625 Combine like terms: 17.5 + 1.5625 = 19.0625 1.5625 + -2.5x + x2 = 19.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 19.0625 Calculate the square root of the right side: 4.366062299 Break this problem into two subproblems by setting (x + -1.25) equal to 4.366062299 and -4.366062299.Subproblem 1
x + -1.25 = 4.366062299 Simplifying x + -1.25 = 4.366062299 Reorder the terms: -1.25 + x = 4.366062299 Solving -1.25 + x = 4.366062299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 4.366062299 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 4.366062299 + 1.25 x = 4.366062299 + 1.25 Combine like terms: 4.366062299 + 1.25 = 5.616062299 x = 5.616062299 Simplifying x = 5.616062299Subproblem 2
x + -1.25 = -4.366062299 Simplifying x + -1.25 = -4.366062299 Reorder the terms: -1.25 + x = -4.366062299 Solving -1.25 + x = -4.366062299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -4.366062299 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -4.366062299 + 1.25 x = -4.366062299 + 1.25 Combine like terms: -4.366062299 + 1.25 = -3.116062299 x = -3.116062299 Simplifying x = -3.116062299Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.616062299, -3.116062299}
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