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Simplifying 0 = 5x2 + 17x + -25 Reorder the terms: 0 = -25 + 17x + 5x2 Solving 0 = -25 + 17x + 5x2 Solving for variable 'x'. Combine like terms: 0 + 25 = 25 25 + -17x + -5x2 = -25 + 17x + 5x2 + 25 + -17x + -5x2 Reorder the terms: 25 + -17x + -5x2 = -25 + 25 + 17x + -17x + 5x2 + -5x2 Combine like terms: -25 + 25 = 0 25 + -17x + -5x2 = 0 + 17x + -17x + 5x2 + -5x2 25 + -17x + -5x2 = 17x + -17x + 5x2 + -5x2 Combine like terms: 17x + -17x = 0 25 + -17x + -5x2 = 0 + 5x2 + -5x2 25 + -17x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 25 + -17x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -5 + 3.4x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 3.4x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 3.4x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3.4x + x2 = 0 + 5 3.4x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 3.4x + x2 = 5 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 = 5 + 2.89 Reorder the terms: 2.89 + 3.4x + x2 = 5 + 2.89 Combine like terms: 5 + 2.89 = 7.89 2.89 + 3.4x + x2 = 7.89 Factor a perfect square on the left side: (x + 1.7)(x + 1.7) = 7.89 Calculate the square root of the right side: 2.808914381 Break this problem into two subproblems by setting (x + 1.7) equal to 2.808914381 and -2.808914381.Subproblem 1
x + 1.7 = 2.808914381 Simplifying x + 1.7 = 2.808914381 Reorder the terms: 1.7 + x = 2.808914381 Solving 1.7 + x = 2.808914381 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 = 2.808914381 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = 2.808914381 + -1.7 x = 2.808914381 + -1.7 Combine like terms: 2.808914381 + -1.7 = 1.108914381 x = 1.108914381 Simplifying x = 1.108914381Subproblem 2
x + 1.7 = -2.808914381 Simplifying x + 1.7 = -2.808914381 Reorder the terms: 1.7 + x = -2.808914381 Solving 1.7 + x = -2.808914381 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 = -2.808914381 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = -2.808914381 + -1.7 x = -2.808914381 + -1.7 Combine like terms: -2.808914381 + -1.7 = -4.508914381 x = -4.508914381 Simplifying x = -4.508914381Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.108914381, -4.508914381}
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