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Simplifying 25x2 + 85x + -26 = 0 Reorder the terms: -26 + 85x + 25x2 = 0 Solving -26 + 85x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1.04 + 3.4x + x2 = 0 Move the constant term to the right: Add '1.04' to each side of the equation. -1.04 + 3.4x + 1.04 + x2 = 0 + 1.04 Reorder the terms: -1.04 + 1.04 + 3.4x + x2 = 0 + 1.04 Combine like terms: -1.04 + 1.04 = 0.00 0.00 + 3.4x + x2 = 0 + 1.04 3.4x + x2 = 0 + 1.04 Combine like terms: 0 + 1.04 = 1.04 3.4x + x2 = 1.04 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 = 1.04 + 2.89 Reorder the terms: 2.89 + 3.4x + x2 = 1.04 + 2.89 Combine like terms: 1.04 + 2.89 = 3.93 2.89 + 3.4x + x2 = 3.93 Factor a perfect square on the left side: (x + 1.7)(x + 1.7) = 3.93 Calculate the square root of the right side: 1.98242276 Break this problem into two subproblems by setting (x + 1.7) equal to 1.98242276 and -1.98242276.Subproblem 1
x + 1.7 = 1.98242276 Simplifying x + 1.7 = 1.98242276 Reorder the terms: 1.7 + x = 1.98242276 Solving 1.7 + x = 1.98242276 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 = 1.98242276 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = 1.98242276 + -1.7 x = 1.98242276 + -1.7 Combine like terms: 1.98242276 + -1.7 = 0.28242276 x = 0.28242276 Simplifying x = 0.28242276Subproblem 2
x + 1.7 = -1.98242276 Simplifying x + 1.7 = -1.98242276 Reorder the terms: 1.7 + x = -1.98242276 Solving 1.7 + x = -1.98242276 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 = -1.98242276 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = -1.98242276 + -1.7 x = -1.98242276 + -1.7 Combine like terms: -1.98242276 + -1.7 = -3.68242276 x = -3.68242276 Simplifying x = -3.68242276Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.28242276, -3.68242276}
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