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Simplifying 0 = 5x2 + -5x + -1 Reorder the terms: 0 = -1 + -5x + 5x2 Solving 0 = -1 + -5x + 5x2 Solving for variable 'x'. Combine like terms: 0 + 1 = 1 1 + 5x + -5x2 = -1 + -5x + 5x2 + 1 + 5x + -5x2 Reorder the terms: 1 + 5x + -5x2 = -1 + 1 + -5x + 5x + 5x2 + -5x2 Combine like terms: -1 + 1 = 0 1 + 5x + -5x2 = 0 + -5x + 5x + 5x2 + -5x2 1 + 5x + -5x2 = -5x + 5x + 5x2 + -5x2 Combine like terms: -5x + 5x = 0 1 + 5x + -5x2 = 0 + 5x2 + -5x2 1 + 5x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 1 + 5x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.2 + -1x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -1x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -1x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -1x + x2 = 0 + 0.2 -1x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -1x + x2 = 0.2 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.2 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.2 + 0.25 Combine like terms: 0.2 + 0.25 = 0.45 0.25 + -1x + x2 = 0.45 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.45 Calculate the square root of the right side: 0.670820393 Break this problem into two subproblems by setting (x + -0.5) equal to 0.670820393 and -0.670820393.Subproblem 1
x + -0.5 = 0.670820393 Simplifying x + -0.5 = 0.670820393 Reorder the terms: -0.5 + x = 0.670820393 Solving -0.5 + x = 0.670820393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.670820393 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.670820393 + 0.5 x = 0.670820393 + 0.5 Combine like terms: 0.670820393 + 0.5 = 1.170820393 x = 1.170820393 Simplifying x = 1.170820393Subproblem 2
x + -0.5 = -0.670820393 Simplifying x + -0.5 = -0.670820393 Reorder the terms: -0.5 + x = -0.670820393 Solving -0.5 + x = -0.670820393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.670820393 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.670820393 + 0.5 x = -0.670820393 + 0.5 Combine like terms: -0.670820393 + 0.5 = -0.170820393 x = -0.170820393 Simplifying x = -0.170820393Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.170820393, -0.170820393}
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