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Simplifying x2 + 63x = 36 Reorder the terms: 63x + x2 = 36 Solving 63x + x2 = 36 Solving for variable 'x'. Reorder the terms: -36 + 63x + x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 63x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 63x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 63x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 63x + x2 = 0 + 36 63x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 63x + x2 = 36 The x term is 63x. Take half its coefficient (31.5). Square it (992.25) and add it to both sides. Add '992.25' to each side of the equation. 63x + 992.25 + x2 = 36 + 992.25 Reorder the terms: 992.25 + 63x + x2 = 36 + 992.25 Combine like terms: 36 + 992.25 = 1028.25 992.25 + 63x + x2 = 1028.25 Factor a perfect square on the left side: (x + 31.5)(x + 31.5) = 1028.25 Calculate the square root of the right side: 32.06633749 Break this problem into two subproblems by setting (x + 31.5) equal to 32.06633749 and -32.06633749.Subproblem 1
x + 31.5 = 32.06633749 Simplifying x + 31.5 = 32.06633749 Reorder the terms: 31.5 + x = 32.06633749 Solving 31.5 + x = 32.06633749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.5' to each side of the equation. 31.5 + -31.5 + x = 32.06633749 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + x = 32.06633749 + -31.5 x = 32.06633749 + -31.5 Combine like terms: 32.06633749 + -31.5 = 0.56633749 x = 0.56633749 Simplifying x = 0.56633749Subproblem 2
x + 31.5 = -32.06633749 Simplifying x + 31.5 = -32.06633749 Reorder the terms: 31.5 + x = -32.06633749 Solving 31.5 + x = -32.06633749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.5' to each side of the equation. 31.5 + -31.5 + x = -32.06633749 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + x = -32.06633749 + -31.5 x = -32.06633749 + -31.5 Combine like terms: -32.06633749 + -31.5 = -63.56633749 x = -63.56633749 Simplifying x = -63.56633749Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.56633749, -63.56633749}
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