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Simplifying 5x2 + -20x = 8 Reorder the terms: -20x + 5x2 = 8 Solving -20x + 5x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -20x + 5x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -20x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + -4x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -4x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -4x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -4x + x2 = 0 + 1.6 -4x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -4x + x2 = 1.6 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 = 1.6 + 4 Reorder the terms: 4 + -4x + x2 = 1.6 + 4 Combine like terms: 1.6 + 4 = 5.6 4 + -4x + x2 = 5.6 Factor a perfect square on the left side: (x + -2)(x + -2) = 5.6 Calculate the square root of the right side: 2.366431913 Break this problem into two subproblems by setting (x + -2) equal to 2.366431913 and -2.366431913.Subproblem 1
x + -2 = 2.366431913 Simplifying x + -2 = 2.366431913 Reorder the terms: -2 + x = 2.366431913 Solving -2 + x = 2.366431913 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 = 2.366431913 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.366431913 + 2 x = 2.366431913 + 2 Combine like terms: 2.366431913 + 2 = 4.366431913 x = 4.366431913 Simplifying x = 4.366431913Subproblem 2
x + -2 = -2.366431913 Simplifying x + -2 = -2.366431913 Reorder the terms: -2 + x = -2.366431913 Solving -2 + x = -2.366431913 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 = -2.366431913 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.366431913 + 2 x = -2.366431913 + 2 Combine like terms: -2.366431913 + 2 = -0.366431913 x = -0.366431913 Simplifying x = -0.366431913Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.366431913, -0.366431913}
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