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Simplifying x2 + -13x = 7 Reorder the terms: -13x + x2 = 7 Solving -13x + x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -13x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -13x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -13x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -13x + x2 = 0 + 7 -13x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -13x + x2 = 7 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 = 7 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 7 + 42.25 Combine like terms: 7 + 42.25 = 49.25 42.25 + -13x + x2 = 49.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 49.25 Calculate the square root of the right side: 7.017834424 Break this problem into two subproblems by setting (x + -6.5) equal to 7.017834424 and -7.017834424.Subproblem 1
x + -6.5 = 7.017834424 Simplifying x + -6.5 = 7.017834424 Reorder the terms: -6.5 + x = 7.017834424 Solving -6.5 + x = 7.017834424 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 = 7.017834424 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 7.017834424 + 6.5 x = 7.017834424 + 6.5 Combine like terms: 7.017834424 + 6.5 = 13.517834424 x = 13.517834424 Simplifying x = 13.517834424Subproblem 2
x + -6.5 = -7.017834424 Simplifying x + -6.5 = -7.017834424 Reorder the terms: -6.5 + x = -7.017834424 Solving -6.5 + x = -7.017834424 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 = -7.017834424 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -7.017834424 + 6.5 x = -7.017834424 + 6.5 Combine like terms: -7.017834424 + 6.5 = -0.517834424 x = -0.517834424 Simplifying x = -0.517834424Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.517834424, -0.517834424}
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