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Simplifying x2 = 21 + 5x Solving x2 = 21 + 5x Solving for variable 'x'. Reorder the terms: -21 + -5x + x2 = 21 + 5x + -21 + -5x Reorder the terms: -21 + -5x + x2 = 21 + -21 + 5x + -5x Combine like terms: 21 + -21 = 0 -21 + -5x + x2 = 0 + 5x + -5x -21 + -5x + x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -21 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -5x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -5x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -5x + x2 = 0 + 21 -5x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -5x + x2 = 21 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 21 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 21 + 6.25 Combine like terms: 21 + 6.25 = 27.25 6.25 + -5x + x2 = 27.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (x + -2.5) equal to 5.220153254 and -5.220153254.Subproblem 1
x + -2.5 = 5.220153254 Simplifying x + -2.5 = 5.220153254 Reorder the terms: -2.5 + x = 5.220153254 Solving -2.5 + x = 5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 5.220153254 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 5.220153254 + 2.5 x = 5.220153254 + 2.5 Combine like terms: 5.220153254 + 2.5 = 7.720153254 x = 7.720153254 Simplifying x = 7.720153254Subproblem 2
x + -2.5 = -5.220153254 Simplifying x + -2.5 = -5.220153254 Reorder the terms: -2.5 + x = -5.220153254 Solving -2.5 + x = -5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -5.220153254 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -5.220153254 + 2.5 x = -5.220153254 + 2.5 Combine like terms: -5.220153254 + 2.5 = -2.720153254 x = -2.720153254 Simplifying x = -2.720153254Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.720153254, -2.720153254}
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