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Simplifying 2x2 + 60x + 25 = 0 Reorder the terms: 25 + 60x + 2x2 = 0 Solving 25 + 60x + 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'. 12.5 + 30x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + 30x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + 30x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + 30x + x2 = 0 + -12.5 30x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 30x + x2 = -12.5 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = -12.5 + 225 Reorder the terms: 225 + 30x + x2 = -12.5 + 225 Combine like terms: -12.5 + 225 = 212.5 225 + 30x + x2 = 212.5 Factor a perfect square on the left side: (x + 15)(x + 15) = 212.5 Calculate the square root of the right side: 14.577379737 Break this problem into two subproblems by setting (x + 15) equal to 14.577379737 and -14.577379737.Subproblem 1
x + 15 = 14.577379737 Simplifying x + 15 = 14.577379737 Reorder the terms: 15 + x = 14.577379737 Solving 15 + x = 14.577379737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 14.577379737 + -15 Combine like terms: 15 + -15 = 0 0 + x = 14.577379737 + -15 x = 14.577379737 + -15 Combine like terms: 14.577379737 + -15 = -0.422620263 x = -0.422620263 Simplifying x = -0.422620263Subproblem 2
x + 15 = -14.577379737 Simplifying x + 15 = -14.577379737 Reorder the terms: 15 + x = -14.577379737 Solving 15 + x = -14.577379737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -14.577379737 + -15 Combine like terms: 15 + -15 = 0 0 + x = -14.577379737 + -15 x = -14.577379737 + -15 Combine like terms: -14.577379737 + -15 = -29.577379737 x = -29.577379737 Simplifying x = -29.577379737Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.422620263, -29.577379737}
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