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Simplifying X2 + X + -10 = -7X + 5 Reorder the terms: -10 + X + X2 = -7X + 5 Reorder the terms: -10 + X + X2 = 5 + -7X Solving -10 + X + X2 = 5 + -7X Solving for variable 'X'. Reorder the terms: -10 + -5 + X + 7X + X2 = 5 + -7X + -5 + 7X Combine like terms: -10 + -5 = -15 -15 + X + 7X + X2 = 5 + -7X + -5 + 7X Combine like terms: X + 7X = 8X -15 + 8X + X2 = 5 + -7X + -5 + 7X Reorder the terms: -15 + 8X + X2 = 5 + -5 + -7X + 7X Combine like terms: 5 + -5 = 0 -15 + 8X + X2 = 0 + -7X + 7X -15 + 8X + X2 = -7X + 7X Combine like terms: -7X + 7X = 0 -15 + 8X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 8X + 15 + X2 = 0 + 15 Reorder the terms: -15 + 15 + 8X + X2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 8X + X2 = 0 + 15 8X + X2 = 0 + 15 Combine like terms: 0 + 15 = 15 8X + X2 = 15 The X term is 8X. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8X + 16 + X2 = 15 + 16 Reorder the terms: 16 + 8X + X2 = 15 + 16 Combine like terms: 15 + 16 = 31 16 + 8X + X2 = 31 Factor a perfect square on the left side: (X + 4)(X + 4) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (X + 4) equal to 5.567764363 and -5.567764363.Subproblem 1
X + 4 = 5.567764363 Simplifying X + 4 = 5.567764363 Reorder the terms: 4 + X = 5.567764363 Solving 4 + X = 5.567764363 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + X = 5.567764363 + -4 Combine like terms: 4 + -4 = 0 0 + X = 5.567764363 + -4 X = 5.567764363 + -4 Combine like terms: 5.567764363 + -4 = 1.567764363 X = 1.567764363 Simplifying X = 1.567764363Subproblem 2
X + 4 = -5.567764363 Simplifying X + 4 = -5.567764363 Reorder the terms: 4 + X = -5.567764363 Solving 4 + X = -5.567764363 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + X = -5.567764363 + -4 Combine like terms: 4 + -4 = 0 0 + X = -5.567764363 + -4 X = -5.567764363 + -4 Combine like terms: -5.567764363 + -4 = -9.567764363 X = -9.567764363 Simplifying X = -9.567764363Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.567764363, -9.567764363}
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