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Simplifying 0.25x2 + -5x + -7 = 0 Reorder the terms: -7 + -5x + 0.25x2 = 0 Solving -7 + -5x + 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'. -28 + -20x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + -20x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -20x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -20x + x2 = 0 + 28 -20x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -20x + x2 = 28 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 28 + 100 Reorder the terms: 100 + -20x + x2 = 28 + 100 Combine like terms: 28 + 100 = 128 100 + -20x + x2 = 128 Factor a perfect square on the left side: (x + -10)(x + -10) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (x + -10) equal to 11.313708499 and -11.313708499.Subproblem 1
x + -10 = 11.313708499 Simplifying x + -10 = 11.313708499 Reorder the terms: -10 + x = 11.313708499 Solving -10 + x = 11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 11.313708499 + 10 Combine like terms: -10 + 10 = 0 0 + x = 11.313708499 + 10 x = 11.313708499 + 10 Combine like terms: 11.313708499 + 10 = 21.313708499 x = 21.313708499 Simplifying x = 21.313708499Subproblem 2
x + -10 = -11.313708499 Simplifying x + -10 = -11.313708499 Reorder the terms: -10 + x = -11.313708499 Solving -10 + x = -11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -11.313708499 + 10 Combine like terms: -10 + 10 = 0 0 + x = -11.313708499 + 10 x = -11.313708499 + 10 Combine like terms: -11.313708499 + 10 = -1.313708499 x = -1.313708499 Simplifying x = -1.313708499Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.313708499, -1.313708499}
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