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Simplifying x2 + -7x + -288 = 0 Reorder the terms: -288 + -7x + x2 = 0 Solving -288 + -7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '288' to each side of the equation. -288 + -7x + 288 + x2 = 0 + 288 Reorder the terms: -288 + 288 + -7x + x2 = 0 + 288 Combine like terms: -288 + 288 = 0 0 + -7x + x2 = 0 + 288 -7x + x2 = 0 + 288 Combine like terms: 0 + 288 = 288 -7x + x2 = 288 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 = 288 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 288 + 12.25 Combine like terms: 288 + 12.25 = 300.25 12.25 + -7x + x2 = 300.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 300.25 Calculate the square root of the right side: 17.327723451 Break this problem into two subproblems by setting (x + -3.5) equal to 17.327723451 and -17.327723451.Subproblem 1
x + -3.5 = 17.327723451 Simplifying x + -3.5 = 17.327723451 Reorder the terms: -3.5 + x = 17.327723451 Solving -3.5 + x = 17.327723451 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 = 17.327723451 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 17.327723451 + 3.5 x = 17.327723451 + 3.5 Combine like terms: 17.327723451 + 3.5 = 20.827723451 x = 20.827723451 Simplifying x = 20.827723451Subproblem 2
x + -3.5 = -17.327723451 Simplifying x + -3.5 = -17.327723451 Reorder the terms: -3.5 + x = -17.327723451 Solving -3.5 + x = -17.327723451 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 = -17.327723451 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -17.327723451 + 3.5 x = -17.327723451 + 3.5 Combine like terms: -17.327723451 + 3.5 = -13.827723451 x = -13.827723451 Simplifying x = -13.827723451Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.827723451, -13.827723451}
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