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Simplifying x2 + 7x + -3520 = 0 Reorder the terms: -3520 + 7x + x2 = 0 Solving -3520 + 7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3520' to each side of the equation. -3520 + 7x + 3520 + x2 = 0 + 3520 Reorder the terms: -3520 + 3520 + 7x + x2 = 0 + 3520 Combine like terms: -3520 + 3520 = 0 0 + 7x + x2 = 0 + 3520 7x + x2 = 0 + 3520 Combine like terms: 0 + 3520 = 3520 7x + x2 = 3520 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 3520 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 3520 + 12.25 Combine like terms: 3520 + 12.25 = 3532.25 12.25 + 7x + x2 = 3532.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 3532.25 Calculate the square root of the right side: 59.432735088 Break this problem into two subproblems by setting (x + 3.5) equal to 59.432735088 and -59.432735088.Subproblem 1
x + 3.5 = 59.432735088 Simplifying x + 3.5 = 59.432735088 Reorder the terms: 3.5 + x = 59.432735088 Solving 3.5 + x = 59.432735088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 59.432735088 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 59.432735088 + -3.5 x = 59.432735088 + -3.5 Combine like terms: 59.432735088 + -3.5 = 55.932735088 x = 55.932735088 Simplifying x = 55.932735088Subproblem 2
x + 3.5 = -59.432735088 Simplifying x + 3.5 = -59.432735088 Reorder the terms: 3.5 + x = -59.432735088 Solving 3.5 + x = -59.432735088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -59.432735088 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -59.432735088 + -3.5 x = -59.432735088 + -3.5 Combine like terms: -59.432735088 + -3.5 = -62.932735088 x = -62.932735088 Simplifying x = -62.932735088Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.932735088, -62.932735088}
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