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Simplifying 2x2 + 15x + -150 = 0 Reorder the terms: -150 + 15x + 2x2 = 0 Solving -150 + 15x + 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'. -75 + 7.5x + x2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + 7.5x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 7.5x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 7.5x + x2 = 0 + 75 7.5x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 7.5x + x2 = 75 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 75 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 75 + 14.0625 Combine like terms: 75 + 14.0625 = 89.0625 14.0625 + 7.5x + x2 = 89.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 89.0625 Calculate the square root of the right side: 9.437293044 Break this problem into two subproblems by setting (x + 3.75) equal to 9.437293044 and -9.437293044.Subproblem 1
x + 3.75 = 9.437293044 Simplifying x + 3.75 = 9.437293044 Reorder the terms: 3.75 + x = 9.437293044 Solving 3.75 + x = 9.437293044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 9.437293044 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 9.437293044 + -3.75 x = 9.437293044 + -3.75 Combine like terms: 9.437293044 + -3.75 = 5.687293044 x = 5.687293044 Simplifying x = 5.687293044Subproblem 2
x + 3.75 = -9.437293044 Simplifying x + 3.75 = -9.437293044 Reorder the terms: 3.75 + x = -9.437293044 Solving 3.75 + x = -9.437293044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -9.437293044 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -9.437293044 + -3.75 x = -9.437293044 + -3.75 Combine like terms: -9.437293044 + -3.75 = -13.187293044 x = -13.187293044 Simplifying x = -13.187293044Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.687293044, -13.187293044}
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