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Simplifying 13x2 + 21x = 5x2 + 22 Reorder the terms: 21x + 13x2 = 5x2 + 22 Reorder the terms: 21x + 13x2 = 22 + 5x2 Solving 21x + 13x2 = 22 + 5x2 Solving for variable 'x'. Reorder the terms: -22 + 21x + 13x2 + -5x2 = 22 + 5x2 + -22 + -5x2 Combine like terms: 13x2 + -5x2 = 8x2 -22 + 21x + 8x2 = 22 + 5x2 + -22 + -5x2 Reorder the terms: -22 + 21x + 8x2 = 22 + -22 + 5x2 + -5x2 Combine like terms: 22 + -22 = 0 -22 + 21x + 8x2 = 0 + 5x2 + -5x2 -22 + 21x + 8x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -22 + 21x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.75 + 2.625x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 2.625x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 2.625x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 2.625x + x2 = 0 + 2.75 2.625x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 2.625x + x2 = 2.75 The x term is 2.625x. Take half its coefficient (1.3125). Square it (1.72265625) and add it to both sides. Add '1.72265625' to each side of the equation. 2.625x + 1.72265625 + x2 = 2.75 + 1.72265625 Reorder the terms: 1.72265625 + 2.625x + x2 = 2.75 + 1.72265625 Combine like terms: 2.75 + 1.72265625 = 4.47265625 1.72265625 + 2.625x + x2 = 4.47265625 Factor a perfect square on the left side: (x + 1.3125)(x + 1.3125) = 4.47265625 Calculate the square root of the right side: 2.114865539 Break this problem into two subproblems by setting (x + 1.3125) equal to 2.114865539 and -2.114865539.Subproblem 1
x + 1.3125 = 2.114865539 Simplifying x + 1.3125 = 2.114865539 Reorder the terms: 1.3125 + x = 2.114865539 Solving 1.3125 + x = 2.114865539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3125' to each side of the equation. 1.3125 + -1.3125 + x = 2.114865539 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + x = 2.114865539 + -1.3125 x = 2.114865539 + -1.3125 Combine like terms: 2.114865539 + -1.3125 = 0.802365539 x = 0.802365539 Simplifying x = 0.802365539Subproblem 2
x + 1.3125 = -2.114865539 Simplifying x + 1.3125 = -2.114865539 Reorder the terms: 1.3125 + x = -2.114865539 Solving 1.3125 + x = -2.114865539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3125' to each side of the equation. 1.3125 + -1.3125 + x = -2.114865539 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + x = -2.114865539 + -1.3125 x = -2.114865539 + -1.3125 Combine like terms: -2.114865539 + -1.3125 = -3.427365539 x = -3.427365539 Simplifying x = -3.427365539Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.802365539, -3.427365539}
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