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Simplifying -5x2 + 20x + -13 = 0 Reorder the terms: -13 + 20x + -5x2 = 0 Solving -13 + 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'. 2.6 + -4x + x2 = 0 Move the constant term to the right: Add '-2.6' to each side of the equation. 2.6 + -4x + -2.6 + x2 = 0 + -2.6 Reorder the terms: 2.6 + -2.6 + -4x + x2 = 0 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + -4x + x2 = 0 + -2.6 -4x + x2 = 0 + -2.6 Combine like terms: 0 + -2.6 = -2.6 -4x + x2 = -2.6 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 = -2.6 + 4 Reorder the terms: 4 + -4x + x2 = -2.6 + 4 Combine like terms: -2.6 + 4 = 1.4 4 + -4x + x2 = 1.4 Factor a perfect square on the left side: (x + -2)(x + -2) = 1.4 Calculate the square root of the right side: 1.183215957 Break this problem into two subproblems by setting (x + -2) equal to 1.183215957 and -1.183215957.Subproblem 1
x + -2 = 1.183215957 Simplifying x + -2 = 1.183215957 Reorder the terms: -2 + x = 1.183215957 Solving -2 + x = 1.183215957 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 = 1.183215957 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.183215957 + 2 x = 1.183215957 + 2 Combine like terms: 1.183215957 + 2 = 3.183215957 x = 3.183215957 Simplifying x = 3.183215957Subproblem 2
x + -2 = -1.183215957 Simplifying x + -2 = -1.183215957 Reorder the terms: -2 + x = -1.183215957 Solving -2 + x = -1.183215957 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 = -1.183215957 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.183215957 + 2 x = -1.183215957 + 2 Combine like terms: -1.183215957 + 2 = 0.816784043 x = 0.816784043 Simplifying x = 0.816784043Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.183215957, 0.816784043}
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