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Simplifying 0 = -5x2 + 20x + 2 Reorder the terms: 0 = 2 + 20x + -5x2 Solving 0 = 2 + 20x + -5x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + -20x + 5x2 = 2 + 20x + -5x2 + -2 + -20x + 5x2 Reorder the terms: -2 + -20x + 5x2 = 2 + -2 + 20x + -20x + -5x2 + 5x2 Combine like terms: 2 + -2 = 0 -2 + -20x + 5x2 = 0 + 20x + -20x + -5x2 + 5x2 -2 + -20x + 5x2 = 20x + -20x + -5x2 + 5x2 Combine like terms: 20x + -20x = 0 -2 + -20x + 5x2 = 0 + -5x2 + 5x2 -2 + -20x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -2 + -20x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -4x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -4x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -4x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -4x + x2 = 0 + 0.4 -4x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -4x + x2 = 0.4 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 = 0.4 + 4 Reorder the terms: 4 + -4x + x2 = 0.4 + 4 Combine like terms: 0.4 + 4 = 4.4 4 + -4x + x2 = 4.4 Factor a perfect square on the left side: (x + -2)(x + -2) = 4.4 Calculate the square root of the right side: 2.097617696 Break this problem into two subproblems by setting (x + -2) equal to 2.097617696 and -2.097617696.Subproblem 1
x + -2 = 2.097617696 Simplifying x + -2 = 2.097617696 Reorder the terms: -2 + x = 2.097617696 Solving -2 + x = 2.097617696 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 = 2.097617696 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.097617696 + 2 x = 2.097617696 + 2 Combine like terms: 2.097617696 + 2 = 4.097617696 x = 4.097617696 Simplifying x = 4.097617696Subproblem 2
x + -2 = -2.097617696 Simplifying x + -2 = -2.097617696 Reorder the terms: -2 + x = -2.097617696 Solving -2 + x = -2.097617696 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 = -2.097617696 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.097617696 + 2 x = -2.097617696 + 2 Combine like terms: -2.097617696 + 2 = -0.097617696 x = -0.097617696 Simplifying x = -0.097617696Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.097617696, -0.097617696}
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