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Simplifying 2x2 + 15x + -450 = 0 Reorder the terms: -450 + 15x + 2x2 = 0 Solving -450 + 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'. -225 + 7.5x + x2 = 0 Move the constant term to the right: Add '225' to each side of the equation. -225 + 7.5x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + 7.5x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + 7.5x + x2 = 0 + 225 7.5x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 7.5x + x2 = 225 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 = 225 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 225 + 14.0625 Combine like terms: 225 + 14.0625 = 239.0625 14.0625 + 7.5x + x2 = 239.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 239.0625 Calculate the square root of the right side: 15.461646096 Break this problem into two subproblems by setting (x + 3.75) equal to 15.461646096 and -15.461646096.Subproblem 1
x + 3.75 = 15.461646096 Simplifying x + 3.75 = 15.461646096 Reorder the terms: 3.75 + x = 15.461646096 Solving 3.75 + x = 15.461646096 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 = 15.461646096 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 15.461646096 + -3.75 x = 15.461646096 + -3.75 Combine like terms: 15.461646096 + -3.75 = 11.711646096 x = 11.711646096 Simplifying x = 11.711646096Subproblem 2
x + 3.75 = -15.461646096 Simplifying x + 3.75 = -15.461646096 Reorder the terms: 3.75 + x = -15.461646096 Solving 3.75 + x = -15.461646096 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 = -15.461646096 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -15.461646096 + -3.75 x = -15.461646096 + -3.75 Combine like terms: -15.461646096 + -3.75 = -19.211646096 x = -19.211646096 Simplifying x = -19.211646096Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.711646096, -19.211646096}
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