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Simplifying -24 + -7x + x2 = 0 Solving -24 + -7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -7x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -7x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -7x + x2 = 0 + 24 -7x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -7x + x2 = 24 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 = 24 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 24 + 12.25 Combine like terms: 24 + 12.25 = 36.25 12.25 + -7x + x2 = 36.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (x + -3.5) equal to 6.020797289 and -6.020797289.Subproblem 1
x + -3.5 = 6.020797289 Simplifying x + -3.5 = 6.020797289 Reorder the terms: -3.5 + x = 6.020797289 Solving -3.5 + x = 6.020797289 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 = 6.020797289 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 6.020797289 + 3.5 x = 6.020797289 + 3.5 Combine like terms: 6.020797289 + 3.5 = 9.520797289 x = 9.520797289 Simplifying x = 9.520797289Subproblem 2
x + -3.5 = -6.020797289 Simplifying x + -3.5 = -6.020797289 Reorder the terms: -3.5 + x = -6.020797289 Solving -3.5 + x = -6.020797289 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 = -6.020797289 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -6.020797289 + 3.5 x = -6.020797289 + 3.5 Combine like terms: -6.020797289 + 3.5 = -2.520797289 x = -2.520797289 Simplifying x = -2.520797289Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.520797289, -2.520797289}
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