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Simplifying x2 + 8x = 624 Reorder the terms: 8x + x2 = 624 Solving 8x + x2 = 624 Solving for variable 'x'. Reorder the terms: -624 + 8x + x2 = 624 + -624 Combine like terms: 624 + -624 = 0 -624 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '624' to each side of the equation. -624 + 8x + 624 + x2 = 0 + 624 Reorder the terms: -624 + 624 + 8x + x2 = 0 + 624 Combine like terms: -624 + 624 = 0 0 + 8x + x2 = 0 + 624 8x + x2 = 0 + 624 Combine like terms: 0 + 624 = 624 8x + x2 = 624 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 624 + 16 Reorder the terms: 16 + 8x + x2 = 624 + 16 Combine like terms: 624 + 16 = 640 16 + 8x + x2 = 640 Factor a perfect square on the left side: (x + 4)(x + 4) = 640 Calculate the square root of the right side: 25.298221281 Break this problem into two subproblems by setting (x + 4) equal to 25.298221281 and -25.298221281.Subproblem 1
x + 4 = 25.298221281 Simplifying x + 4 = 25.298221281 Reorder the terms: 4 + x = 25.298221281 Solving 4 + x = 25.298221281 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 25.298221281 + -4 Combine like terms: 4 + -4 = 0 0 + x = 25.298221281 + -4 x = 25.298221281 + -4 Combine like terms: 25.298221281 + -4 = 21.298221281 x = 21.298221281 Simplifying x = 21.298221281Subproblem 2
x + 4 = -25.298221281 Simplifying x + 4 = -25.298221281 Reorder the terms: 4 + x = -25.298221281 Solving 4 + x = -25.298221281 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -25.298221281 + -4 Combine like terms: 4 + -4 = 0 0 + x = -25.298221281 + -4 x = -25.298221281 + -4 Combine like terms: -25.298221281 + -4 = -29.298221281 x = -29.298221281 Simplifying x = -29.298221281Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.298221281, -29.298221281}
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