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Simplifying 3x2 = 99 + 21x Solving 3x2 = 99 + 21x Solving for variable 'x'. Reorder the terms: -99 + -21x + 3x2 = 99 + 21x + -99 + -21x Reorder the terms: -99 + -21x + 3x2 = 99 + -99 + 21x + -21x Combine like terms: 99 + -99 = 0 -99 + -21x + 3x2 = 0 + 21x + -21x -99 + -21x + 3x2 = 21x + -21x Combine like terms: 21x + -21x = 0 -99 + -21x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-33 + -7x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-33 + -7x + x2)' equal to zero and attempt to solve: Simplifying -33 + -7x + x2 = 0 Solving -33 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + -7x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + -7x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + -7x + x2 = 0 + 33 -7x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 -7x + x2 = 33 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 = 33 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 33 + 12.25 Combine like terms: 33 + 12.25 = 45.25 12.25 + -7x + x2 = 45.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (x + -3.5) equal to 6.726812024 and -6.726812024.Subproblem 1
x + -3.5 = 6.726812024 Simplifying x + -3.5 = 6.726812024 Reorder the terms: -3.5 + x = 6.726812024 Solving -3.5 + x = 6.726812024 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 = 6.726812024 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 6.726812024 + 3.5 x = 6.726812024 + 3.5 Combine like terms: 6.726812024 + 3.5 = 10.226812024 x = 10.226812024 Simplifying x = 10.226812024Subproblem 2
x + -3.5 = -6.726812024 Simplifying x + -3.5 = -6.726812024 Reorder the terms: -3.5 + x = -6.726812024 Solving -3.5 + x = -6.726812024 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 = -6.726812024 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -6.726812024 + 3.5 x = -6.726812024 + 3.5 Combine like terms: -6.726812024 + 3.5 = -3.226812024 x = -3.226812024 Simplifying x = -3.226812024Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.226812024, -3.226812024}Solution
x = {10.226812024, -3.226812024}
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