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Simplifying -5x2 + 20x + 1.6 = 0 Reorder the terms: 1.6 + 20x + -5x2 = 0 Solving 1.6 + 20x + -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'. -0.32 + -4x + x2 = 0 Move the constant term to the right: Add '0.32' to each side of the equation. -0.32 + -4x + 0.32 + x2 = 0 + 0.32 Reorder the terms: -0.32 + 0.32 + -4x + x2 = 0 + 0.32 Combine like terms: -0.32 + 0.32 = 0.00 0.00 + -4x + x2 = 0 + 0.32 -4x + x2 = 0 + 0.32 Combine like terms: 0 + 0.32 = 0.32 -4x + x2 = 0.32 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 = 0.32 + 4 Reorder the terms: 4 + -4x + x2 = 0.32 + 4 Combine like terms: 0.32 + 4 = 4.32 4 + -4x + x2 = 4.32 Factor a perfect square on the left side: (x + -2)(x + -2) = 4.32 Calculate the square root of the right side: 2.078460969 Break this problem into two subproblems by setting (x + -2) equal to 2.078460969 and -2.078460969.Subproblem 1
x + -2 = 2.078460969 Simplifying x + -2 = 2.078460969 Reorder the terms: -2 + x = 2.078460969 Solving -2 + x = 2.078460969 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 = 2.078460969 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.078460969 + 2 x = 2.078460969 + 2 Combine like terms: 2.078460969 + 2 = 4.078460969 x = 4.078460969 Simplifying x = 4.078460969Subproblem 2
x + -2 = -2.078460969 Simplifying x + -2 = -2.078460969 Reorder the terms: -2 + x = -2.078460969 Solving -2 + x = -2.078460969 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 = -2.078460969 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.078460969 + 2 x = -2.078460969 + 2 Combine like terms: -2.078460969 + 2 = -0.078460969 x = -0.078460969 Simplifying x = -0.078460969Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.078460969, -0.078460969}
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