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Simplifying x2 + -13x + -4 = 0 Reorder the terms: -4 + -13x + x2 = 0 Solving -4 + -13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -13x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -13x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -13x + x2 = 0 + 4 -13x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -13x + x2 = 4 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 4 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 4 + 42.25 Combine like terms: 4 + 42.25 = 46.25 42.25 + -13x + x2 = 46.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (x + -6.5) equal to 6.800735254 and -6.800735254.Subproblem 1
x + -6.5 = 6.800735254 Simplifying x + -6.5 = 6.800735254 Reorder the terms: -6.5 + x = 6.800735254 Solving -6.5 + x = 6.800735254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 6.800735254 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 6.800735254 + 6.5 x = 6.800735254 + 6.5 Combine like terms: 6.800735254 + 6.5 = 13.300735254 x = 13.300735254 Simplifying x = 13.300735254Subproblem 2
x + -6.5 = -6.800735254 Simplifying x + -6.5 = -6.800735254 Reorder the terms: -6.5 + x = -6.800735254 Solving -6.5 + x = -6.800735254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -6.800735254 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -6.800735254 + 6.5 x = -6.800735254 + 6.5 Combine like terms: -6.800735254 + 6.5 = -0.300735254 x = -0.300735254 Simplifying x = -0.300735254Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.300735254, -0.300735254}
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