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Simplifying -5x2 + 10x + 16 = 0 Reorder the terms: 16 + 10x + -5x2 = 0 Solving 16 + 10x + -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'. -3.2 + -2x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + -2x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + -2x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + -2x + x2 = 0 + 3.2 -2x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 -2x + x2 = 3.2 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 3.2 + 1 Reorder the terms: 1 + -2x + x2 = 3.2 + 1 Combine like terms: 3.2 + 1 = 4.2 1 + -2x + x2 = 4.2 Factor a perfect square on the left side: (x + -1)(x + -1) = 4.2 Calculate the square root of the right side: 2.049390153 Break this problem into two subproblems by setting (x + -1) equal to 2.049390153 and -2.049390153.Subproblem 1
x + -1 = 2.049390153 Simplifying x + -1 = 2.049390153 Reorder the terms: -1 + x = 2.049390153 Solving -1 + x = 2.049390153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.049390153 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.049390153 + 1 x = 2.049390153 + 1 Combine like terms: 2.049390153 + 1 = 3.049390153 x = 3.049390153 Simplifying x = 3.049390153Subproblem 2
x + -1 = -2.049390153 Simplifying x + -1 = -2.049390153 Reorder the terms: -1 + x = -2.049390153 Solving -1 + x = -2.049390153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.049390153 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.049390153 + 1 x = -2.049390153 + 1 Combine like terms: -2.049390153 + 1 = -1.049390153 x = -1.049390153 Simplifying x = -1.049390153Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.049390153, -1.049390153}
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