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Simplifying -2x2 + -8x + 13 = 0 Reorder the terms: 13 + -8x + -2x2 = 0 Solving 13 + -8x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -6.5 + 4x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + 4x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + 4x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + 4x + x2 = 0 + 6.5 4x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 4x + x2 = 6.5 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 = 6.5 + 4 Reorder the terms: 4 + 4x + x2 = 6.5 + 4 Combine like terms: 6.5 + 4 = 10.5 4 + 4x + x2 = 10.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 10.5 Calculate the square root of the right side: 3.240370349 Break this problem into two subproblems by setting (x + 2) equal to 3.240370349 and -3.240370349.Subproblem 1
x + 2 = 3.240370349 Simplifying x + 2 = 3.240370349 Reorder the terms: 2 + x = 3.240370349 Solving 2 + x = 3.240370349 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 = 3.240370349 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.240370349 + -2 x = 3.240370349 + -2 Combine like terms: 3.240370349 + -2 = 1.240370349 x = 1.240370349 Simplifying x = 1.240370349Subproblem 2
x + 2 = -3.240370349 Simplifying x + 2 = -3.240370349 Reorder the terms: 2 + x = -3.240370349 Solving 2 + x = -3.240370349 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 = -3.240370349 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.240370349 + -2 x = -3.240370349 + -2 Combine like terms: -3.240370349 + -2 = -5.240370349 x = -5.240370349 Simplifying x = -5.240370349Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.240370349, -5.240370349}
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