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Simplifying 25x2 + -16x + -5 = 0 Reorder the terms: -5 + -16x + 25x2 = 0 Solving -5 + -16x + 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'. -0.2 + -0.64x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.64x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.64x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.64x + x2 = 0 + 0.2 -0.64x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.64x + x2 = 0.2 The x term is -0.64x. Take half its coefficient (-0.32). Square it (0.1024) and add it to both sides. Add '0.1024' to each side of the equation. -0.64x + 0.1024 + x2 = 0.2 + 0.1024 Reorder the terms: 0.1024 + -0.64x + x2 = 0.2 + 0.1024 Combine like terms: 0.2 + 0.1024 = 0.3024 0.1024 + -0.64x + x2 = 0.3024 Factor a perfect square on the left side: (x + -0.32)(x + -0.32) = 0.3024 Calculate the square root of the right side: 0.549909083 Break this problem into two subproblems by setting (x + -0.32) equal to 0.549909083 and -0.549909083.Subproblem 1
x + -0.32 = 0.549909083 Simplifying x + -0.32 = 0.549909083 Reorder the terms: -0.32 + x = 0.549909083 Solving -0.32 + x = 0.549909083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.32' to each side of the equation. -0.32 + 0.32 + x = 0.549909083 + 0.32 Combine like terms: -0.32 + 0.32 = 0.00 0.00 + x = 0.549909083 + 0.32 x = 0.549909083 + 0.32 Combine like terms: 0.549909083 + 0.32 = 0.869909083 x = 0.869909083 Simplifying x = 0.869909083Subproblem 2
x + -0.32 = -0.549909083 Simplifying x + -0.32 = -0.549909083 Reorder the terms: -0.32 + x = -0.549909083 Solving -0.32 + x = -0.549909083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.32' to each side of the equation. -0.32 + 0.32 + x = -0.549909083 + 0.32 Combine like terms: -0.32 + 0.32 = 0.00 0.00 + x = -0.549909083 + 0.32 x = -0.549909083 + 0.32 Combine like terms: -0.549909083 + 0.32 = -0.229909083 x = -0.229909083 Simplifying x = -0.229909083Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.869909083, -0.229909083}
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