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Simplifying 5X2 + -8X + -1 = 0 Reorder the terms: -1 + -8X + 5X2 = 0 Solving -1 + -8X + 5X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -1.6X + X2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -1.6X + 0.2 + X2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -1.6X + X2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -1.6X + X2 = 0 + 0.2 -1.6X + X2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -1.6X + X2 = 0.2 The X term is -1.6X. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6X + 0.64 + X2 = 0.2 + 0.64 Reorder the terms: 0.64 + -1.6X + X2 = 0.2 + 0.64 Combine like terms: 0.2 + 0.64 = 0.84 0.64 + -1.6X + X2 = 0.84 Factor a perfect square on the left side: (X + -0.8)(X + -0.8) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (X + -0.8) equal to 0.916515139 and -0.916515139.Subproblem 1
X + -0.8 = 0.916515139 Simplifying X + -0.8 = 0.916515139 Reorder the terms: -0.8 + X = 0.916515139 Solving -0.8 + X = 0.916515139 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + X = 0.916515139 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + X = 0.916515139 + 0.8 X = 0.916515139 + 0.8 Combine like terms: 0.916515139 + 0.8 = 1.716515139 X = 1.716515139 Simplifying X = 1.716515139Subproblem 2
X + -0.8 = -0.916515139 Simplifying X + -0.8 = -0.916515139 Reorder the terms: -0.8 + X = -0.916515139 Solving -0.8 + X = -0.916515139 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + X = -0.916515139 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + X = -0.916515139 + 0.8 X = -0.916515139 + 0.8 Combine like terms: -0.916515139 + 0.8 = -0.116515139 X = -0.116515139 Simplifying X = -0.116515139Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.716515139, -0.116515139}
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