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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 = 1.313708499 x = 1.313708499 Simplifying x = 1.313708499Subproblem 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 = -21.313708499 x = -21.313708499 Simplifying x = -21.313708499Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.313708499, -21.313708499}
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