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Simplifying x2 + -21x + 15 = -9x + 10 Reorder the terms: 15 + -21x + x2 = -9x + 10 Reorder the terms: 15 + -21x + x2 = 10 + -9x Solving 15 + -21x + x2 = 10 + -9x Solving for variable 'x'. Reorder the terms: 15 + -10 + -21x + 9x + x2 = 10 + -9x + -10 + 9x Combine like terms: 15 + -10 = 5 5 + -21x + 9x + x2 = 10 + -9x + -10 + 9x Combine like terms: -21x + 9x = -12x 5 + -12x + x2 = 10 + -9x + -10 + 9x Reorder the terms: 5 + -12x + x2 = 10 + -10 + -9x + 9x Combine like terms: 10 + -10 = 0 5 + -12x + x2 = 0 + -9x + 9x 5 + -12x + x2 = -9x + 9x Combine like terms: -9x + 9x = 0 5 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -12x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -12x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -12x + x2 = 0 + -5 -12x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -12x + x2 = -5 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -5 + 36 Reorder the terms: 36 + -12x + x2 = -5 + 36 Combine like terms: -5 + 36 = 31 36 + -12x + x2 = 31 Factor a perfect square on the left side: (x + -6)(x + -6) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + -6) equal to 5.567764363 and -5.567764363.Subproblem 1
x + -6 = 5.567764363 Simplifying x + -6 = 5.567764363 Reorder the terms: -6 + x = 5.567764363 Solving -6 + x = 5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 5.567764363 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.567764363 + 6 x = 5.567764363 + 6 Combine like terms: 5.567764363 + 6 = 11.567764363 x = 11.567764363 Simplifying x = 11.567764363Subproblem 2
x + -6 = -5.567764363 Simplifying x + -6 = -5.567764363 Reorder the terms: -6 + x = -5.567764363 Solving -6 + x = -5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -5.567764363 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.567764363 + 6 x = -5.567764363 + 6 Combine like terms: -5.567764363 + 6 = 0.432235637 x = 0.432235637 Simplifying x = 0.432235637Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.567764363, 0.432235637}
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