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Simplifying 0.25x2 + -7x + -24 = 0 Reorder the terms: -24 + -7x + 0.25x2 = 0 Solving -24 + -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'. -96 + -28x + x2 = 0 Move the constant term to the right: Add '96' to each side of the equation. -96 + -28x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + -28x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + -28x + x2 = 0 + 96 -28x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 -28x + x2 = 96 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 = 96 + 196 Reorder the terms: 196 + -28x + x2 = 96 + 196 Combine like terms: 96 + 196 = 292 196 + -28x + x2 = 292 Factor a perfect square on the left side: (x + -14)(x + -14) = 292 Calculate the square root of the right side: 17.088007491 Break this problem into two subproblems by setting (x + -14) equal to 17.088007491 and -17.088007491.Subproblem 1
x + -14 = 17.088007491 Simplifying x + -14 = 17.088007491 Reorder the terms: -14 + x = 17.088007491 Solving -14 + x = 17.088007491 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 = 17.088007491 + 14 Combine like terms: -14 + 14 = 0 0 + x = 17.088007491 + 14 x = 17.088007491 + 14 Combine like terms: 17.088007491 + 14 = 31.088007491 x = 31.088007491 Simplifying x = 31.088007491Subproblem 2
x + -14 = -17.088007491 Simplifying x + -14 = -17.088007491 Reorder the terms: -14 + x = -17.088007491 Solving -14 + x = -17.088007491 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 = -17.088007491 + 14 Combine like terms: -14 + 14 = 0 0 + x = -17.088007491 + 14 x = -17.088007491 + 14 Combine like terms: -17.088007491 + 14 = -3.088007491 x = -3.088007491 Simplifying x = -3.088007491Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.088007491, -3.088007491}
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