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Simplifying 0.25x2 + 1.05x + -1 = 0 Reorder the terms: -1 + 1.05x + 0.25x2 = 0 Solving -1 + 1.05x + 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'. -4 + 4.2x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 4.2x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 4.2x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 4.2x + x2 = 0 + 4 4.2x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 4.2x + x2 = 4 The x term is 4.2x. Take half its coefficient (2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. 4.2x + 4.41 + x2 = 4 + 4.41 Reorder the terms: 4.41 + 4.2x + x2 = 4 + 4.41 Combine like terms: 4 + 4.41 = 8.41 4.41 + 4.2x + x2 = 8.41 Factor a perfect square on the left side: (x + 2.1)(x + 2.1) = 8.41 Calculate the square root of the right side: 2.9 Break this problem into two subproblems by setting (x + 2.1) equal to 2.9 and -2.9.Subproblem 1
x + 2.1 = 2.9 Simplifying x + 2.1 = 2.9 Reorder the terms: 2.1 + x = 2.9 Solving 2.1 + x = 2.9 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + x = 2.9 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = 2.9 + -2.1 x = 2.9 + -2.1 Combine like terms: 2.9 + -2.1 = 0.8 x = 0.8 Simplifying x = 0.8Subproblem 2
x + 2.1 = -2.9 Simplifying x + 2.1 = -2.9 Reorder the terms: 2.1 + x = -2.9 Solving 2.1 + x = -2.9 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + x = -2.9 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = -2.9 + -2.1 x = -2.9 + -2.1 Combine like terms: -2.9 + -2.1 = -5 x = -5 Simplifying x = -5Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8, -5}
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