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Simplifying 0 = 13x + -39 + -1x2 Reorder the terms: 0 = -39 + 13x + -1x2 Solving 0 = -39 + 13x + -1x2 Solving for variable 'x'. Combine like terms: 0 + 39 = 39 39 + -13x + x2 = -39 + 13x + -1x2 + 39 + -13x + x2 Reorder the terms: 39 + -13x + x2 = -39 + 39 + 13x + -13x + -1x2 + x2 Combine like terms: -39 + 39 = 0 39 + -13x + x2 = 0 + 13x + -13x + -1x2 + x2 39 + -13x + x2 = 13x + -13x + -1x2 + x2 Combine like terms: 13x + -13x = 0 39 + -13x + x2 = 0 + -1x2 + x2 39 + -13x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 39 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-39' to each side of the equation. 39 + -13x + -39 + x2 = 0 + -39 Reorder the terms: 39 + -39 + -13x + x2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + -13x + x2 = 0 + -39 -13x + x2 = 0 + -39 Combine like terms: 0 + -39 = -39 -13x + x2 = -39 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 = -39 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -39 + 42.25 Combine like terms: -39 + 42.25 = 3.25 42.25 + -13x + x2 = 3.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + -6.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + -6.5 = 1.802775638 Simplifying x + -6.5 = 1.802775638 Reorder the terms: -6.5 + x = 1.802775638 Solving -6.5 + x = 1.802775638 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 = 1.802775638 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 1.802775638 + 6.5 x = 1.802775638 + 6.5 Combine like terms: 1.802775638 + 6.5 = 8.302775638 x = 8.302775638 Simplifying x = 8.302775638Subproblem 2
x + -6.5 = -1.802775638 Simplifying x + -6.5 = -1.802775638 Reorder the terms: -6.5 + x = -1.802775638 Solving -6.5 + x = -1.802775638 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 = -1.802775638 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -1.802775638 + 6.5 x = -1.802775638 + 6.5 Combine like terms: -1.802775638 + 6.5 = 4.697224362 x = 4.697224362 Simplifying x = 4.697224362Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.302775638, 4.697224362}
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