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Simplifying 0.25x2 + -7x + -15 = 0 Reorder the terms: -15 + -7x + 0.25x2 = 0 Solving -15 + -7x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -60 + -28x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -28x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -28x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -28x + x2 = 0 + 60 -28x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -28x + x2 = 60 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = 60 + 196 Reorder the terms: 196 + -28x + x2 = 60 + 196 Combine like terms: 60 + 196 = 256 196 + -28x + x2 = 256 Factor a perfect square on the left side: (x + -14)(x + -14) = 256 Calculate the square root of the right side: 16 Break this problem into two subproblems by setting (x + -14) equal to 16 and -16.Subproblem 1
x + -14 = 16 Simplifying x + -14 = 16 Reorder the terms: -14 + x = 16 Solving -14 + x = 16 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 16 + 14 Combine like terms: -14 + 14 = 0 0 + x = 16 + 14 x = 16 + 14 Combine like terms: 16 + 14 = 30 x = 30 Simplifying x = 30Subproblem 2
x + -14 = -16 Simplifying x + -14 = -16 Reorder the terms: -14 + x = -16 Solving -14 + x = -16 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -16 + 14 Combine like terms: -14 + 14 = 0 0 + x = -16 + 14 x = -16 + 14 Combine like terms: -16 + 14 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {30, -2}
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