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Simplifying 2x2 + 15x + -20 = 0 Reorder the terms: -20 + 15x + 2x2 = 0 Solving -20 + 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'. -10 + 7.5x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 7.5x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 7.5x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 7.5x + x2 = 0 + 10 7.5x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 7.5x + x2 = 10 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 = 10 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 10 + 14.0625 Combine like terms: 10 + 14.0625 = 24.0625 14.0625 + 7.5x + x2 = 24.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 24.0625 Calculate the square root of the right side: 4.905354218 Break this problem into two subproblems by setting (x + 3.75) equal to 4.905354218 and -4.905354218.Subproblem 1
x + 3.75 = 4.905354218 Simplifying x + 3.75 = 4.905354218 Reorder the terms: 3.75 + x = 4.905354218 Solving 3.75 + x = 4.905354218 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 = 4.905354218 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 4.905354218 + -3.75 x = 4.905354218 + -3.75 Combine like terms: 4.905354218 + -3.75 = 1.155354218 x = 1.155354218 Simplifying x = 1.155354218Subproblem 2
x + 3.75 = -4.905354218 Simplifying x + 3.75 = -4.905354218 Reorder the terms: 3.75 + x = -4.905354218 Solving 3.75 + x = -4.905354218 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 = -4.905354218 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -4.905354218 + -3.75 x = -4.905354218 + -3.75 Combine like terms: -4.905354218 + -3.75 = -8.655354218 x = -8.655354218 Simplifying x = -8.655354218Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.155354218, -8.655354218}
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