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Simplifying 5X2 + -20X = -4 Reorder the terms: -20X + 5X2 = -4 Solving -20X + 5X2 = -4 Solving for variable 'X'. Reorder the terms: 4 + -20X + 5X2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + -20X + 5X2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + -4X + X2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -4X + -0.8 + X2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -4X + X2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -4X + X2 = 0 + -0.8 -4X + X2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -4X + X2 = -0.8 The X term is -4X. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4X + 4 + X2 = -0.8 + 4 Reorder the terms: 4 + -4X + X2 = -0.8 + 4 Combine like terms: -0.8 + 4 = 3.2 4 + -4X + X2 = 3.2 Factor a perfect square on the left side: (X + -2)(X + -2) = 3.2 Calculate the square root of the right side: 1.788854382 Break this problem into two subproblems by setting (X + -2) equal to 1.788854382 and -1.788854382.Subproblem 1
X + -2 = 1.788854382 Simplifying X + -2 = 1.788854382 Reorder the terms: -2 + X = 1.788854382 Solving -2 + X = 1.788854382 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + X = 1.788854382 + 2 Combine like terms: -2 + 2 = 0 0 + X = 1.788854382 + 2 X = 1.788854382 + 2 Combine like terms: 1.788854382 + 2 = 3.788854382 X = 3.788854382 Simplifying X = 3.788854382Subproblem 2
X + -2 = -1.788854382 Simplifying X + -2 = -1.788854382 Reorder the terms: -2 + X = -1.788854382 Solving -2 + X = -1.788854382 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + X = -1.788854382 + 2 Combine like terms: -2 + 2 = 0 0 + X = -1.788854382 + 2 X = -1.788854382 + 2 Combine like terms: -1.788854382 + 2 = 0.211145618 X = 0.211145618 Simplifying X = 0.211145618Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.788854382, 0.211145618}
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