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Simplifying x2 = 13x + 15 Reorder the terms: x2 = 15 + 13x Solving x2 = 15 + 13x Solving for variable 'x'. Reorder the terms: -15 + -13x + x2 = 15 + 13x + -15 + -13x Reorder the terms: -15 + -13x + x2 = 15 + -15 + 13x + -13x Combine like terms: 15 + -15 = 0 -15 + -13x + x2 = 0 + 13x + -13x -15 + -13x + x2 = 13x + -13x Combine like terms: 13x + -13x = 0 -15 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -13x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -13x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -13x + x2 = 0 + 15 -13x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -13x + x2 = 15 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 = 15 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 15 + 42.25 Combine like terms: 15 + 42.25 = 57.25 42.25 + -13x + x2 = 57.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 57.25 Calculate the square root of the right side: 7.566372975 Break this problem into two subproblems by setting (x + -6.5) equal to 7.566372975 and -7.566372975.Subproblem 1
x + -6.5 = 7.566372975 Simplifying x + -6.5 = 7.566372975 Reorder the terms: -6.5 + x = 7.566372975 Solving -6.5 + x = 7.566372975 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 = 7.566372975 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 7.566372975 + 6.5 x = 7.566372975 + 6.5 Combine like terms: 7.566372975 + 6.5 = 14.066372975 x = 14.066372975 Simplifying x = 14.066372975Subproblem 2
x + -6.5 = -7.566372975 Simplifying x + -6.5 = -7.566372975 Reorder the terms: -6.5 + x = -7.566372975 Solving -6.5 + x = -7.566372975 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 = -7.566372975 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -7.566372975 + 6.5 x = -7.566372975 + 6.5 Combine like terms: -7.566372975 + 6.5 = -1.066372975 x = -1.066372975 Simplifying x = -1.066372975Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.066372975, -1.066372975}
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