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Simplifying -0.25x2 + 0.85x + 1 = 0 Reorder the terms: 1 + 0.85x + -0.25x2 = 0 Solving 1 + 0.85x + -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 + -3.4x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -3.4x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -3.4x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3.4x + x2 = 0 + 4 -3.4x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -3.4x + x2 = 4 The x term is -3.4x. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4x + 2.89 + x2 = 4 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = 4 + 2.89 Combine like terms: 4 + 2.89 = 6.89 2.89 + -3.4x + x2 = 6.89 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 6.89 Calculate the square root of the right side: 2.62488095 Break this problem into two subproblems by setting (x + -1.7) equal to 2.62488095 and -2.62488095.Subproblem 1
x + -1.7 = 2.62488095 Simplifying x + -1.7 = 2.62488095 Reorder the terms: -1.7 + x = 2.62488095 Solving -1.7 + x = 2.62488095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = 2.62488095 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 2.62488095 + 1.7 x = 2.62488095 + 1.7 Combine like terms: 2.62488095 + 1.7 = 4.32488095 x = 4.32488095 Simplifying x = 4.32488095Subproblem 2
x + -1.7 = -2.62488095 Simplifying x + -1.7 = -2.62488095 Reorder the terms: -1.7 + x = -2.62488095 Solving -1.7 + x = -2.62488095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = -2.62488095 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -2.62488095 + 1.7 x = -2.62488095 + 1.7 Combine like terms: -2.62488095 + 1.7 = -0.92488095 x = -0.92488095 Simplifying x = -0.92488095Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.32488095, -0.92488095}
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