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Simplifying x2 + -14x + -35 = 5x + 1 Reorder the terms: -35 + -14x + x2 = 5x + 1 Reorder the terms: -35 + -14x + x2 = 1 + 5x Solving -35 + -14x + x2 = 1 + 5x Solving for variable 'x'. Reorder the terms: -35 + -1 + -14x + -5x + x2 = 1 + 5x + -1 + -5x Combine like terms: -35 + -1 = -36 -36 + -14x + -5x + x2 = 1 + 5x + -1 + -5x Combine like terms: -14x + -5x = -19x -36 + -19x + x2 = 1 + 5x + -1 + -5x Reorder the terms: -36 + -19x + x2 = 1 + -1 + 5x + -5x Combine like terms: 1 + -1 = 0 -36 + -19x + x2 = 0 + 5x + -5x -36 + -19x + x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -36 + -19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -19x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -19x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -19x + x2 = 0 + 36 -19x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -19x + x2 = 36 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 36 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 36 + 90.25 Combine like terms: 36 + 90.25 = 126.25 90.25 + -19x + x2 = 126.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 126.25 Calculate the square root of the right side: 11.236102527 Break this problem into two subproblems by setting (x + -9.5) equal to 11.236102527 and -11.236102527.Subproblem 1
x + -9.5 = 11.236102527 Simplifying x + -9.5 = 11.236102527 Reorder the terms: -9.5 + x = 11.236102527 Solving -9.5 + x = 11.236102527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 11.236102527 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 11.236102527 + 9.5 x = 11.236102527 + 9.5 Combine like terms: 11.236102527 + 9.5 = 20.736102527 x = 20.736102527 Simplifying x = 20.736102527Subproblem 2
x + -9.5 = -11.236102527 Simplifying x + -9.5 = -11.236102527 Reorder the terms: -9.5 + x = -11.236102527 Solving -9.5 + x = -11.236102527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -11.236102527 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -11.236102527 + 9.5 x = -11.236102527 + 9.5 Combine like terms: -11.236102527 + 9.5 = -1.736102527 x = -1.736102527 Simplifying x = -1.736102527Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.736102527, -1.736102527}
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