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Simplifying 5x2 + -20x + 1 = 4 Reorder the terms: 1 + -20x + 5x2 = 4 Solving 1 + -20x + 5x2 = 4 Solving for variable 'x'. Reorder the terms: 1 + -4 + -20x + 5x2 = 4 + -4 Combine like terms: 1 + -4 = -3 -3 + -20x + 5x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -3 + -20x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -4x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -4x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -4x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -4x + x2 = 0 + 0.6 -4x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -4x + x2 = 0.6 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 = 0.6 + 4 Reorder the terms: 4 + -4x + x2 = 0.6 + 4 Combine like terms: 0.6 + 4 = 4.6 4 + -4x + x2 = 4.6 Factor a perfect square on the left side: (x + -2)(x + -2) = 4.6 Calculate the square root of the right side: 2.144761059 Break this problem into two subproblems by setting (x + -2) equal to 2.144761059 and -2.144761059.Subproblem 1
x + -2 = 2.144761059 Simplifying x + -2 = 2.144761059 Reorder the terms: -2 + x = 2.144761059 Solving -2 + x = 2.144761059 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 = 2.144761059 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.144761059 + 2 x = 2.144761059 + 2 Combine like terms: 2.144761059 + 2 = 4.144761059 x = 4.144761059 Simplifying x = 4.144761059Subproblem 2
x + -2 = -2.144761059 Simplifying x + -2 = -2.144761059 Reorder the terms: -2 + x = -2.144761059 Solving -2 + x = -2.144761059 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 = -2.144761059 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.144761059 + 2 x = -2.144761059 + 2 Combine like terms: -2.144761059 + 2 = -0.144761059 x = -0.144761059 Simplifying x = -0.144761059Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.144761059, -0.144761059}
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