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Simplifying x2 + 21x = 378 Reorder the terms: 21x + x2 = 378 Solving 21x + x2 = 378 Solving for variable 'x'. Reorder the terms: -378 + 21x + x2 = 378 + -378 Combine like terms: 378 + -378 = 0 -378 + 21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '378' to each side of the equation. -378 + 21x + 378 + x2 = 0 + 378 Reorder the terms: -378 + 378 + 21x + x2 = 0 + 378 Combine like terms: -378 + 378 = 0 0 + 21x + x2 = 0 + 378 21x + x2 = 0 + 378 Combine like terms: 0 + 378 = 378 21x + x2 = 378 The x term is 21x. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21x + 110.25 + x2 = 378 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 378 + 110.25 Combine like terms: 378 + 110.25 = 488.25 110.25 + 21x + x2 = 488.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 488.25 Calculate the square root of the right side: 22.096379794 Break this problem into two subproblems by setting (x + 10.5) equal to 22.096379794 and -22.096379794.Subproblem 1
x + 10.5 = 22.096379794 Simplifying x + 10.5 = 22.096379794 Reorder the terms: 10.5 + x = 22.096379794 Solving 10.5 + x = 22.096379794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 22.096379794 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 22.096379794 + -10.5 x = 22.096379794 + -10.5 Combine like terms: 22.096379794 + -10.5 = 11.596379794 x = 11.596379794 Simplifying x = 11.596379794Subproblem 2
x + 10.5 = -22.096379794 Simplifying x + 10.5 = -22.096379794 Reorder the terms: 10.5 + x = -22.096379794 Solving 10.5 + x = -22.096379794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -22.096379794 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -22.096379794 + -10.5 x = -22.096379794 + -10.5 Combine like terms: -22.096379794 + -10.5 = -32.596379794 x = -32.596379794 Simplifying x = -32.596379794Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.596379794, -32.596379794}
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