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Simplifying 2x2 + -42x = -72 Reorder the terms: -42x + 2x2 = -72 Solving -42x + 2x2 = -72 Solving for variable 'x'. Reorder the terms: 72 + -42x + 2x2 = -72 + 72 Combine like terms: -72 + 72 = 0 72 + -42x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(36 + -21x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(36 + -21x + x2)' equal to zero and attempt to solve: Simplifying 36 + -21x + x2 = 0 Solving 36 + -21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -21x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -21x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -21x + x2 = 0 + -36 -21x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -21x + x2 = -36 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = -36 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -36 + 110.25 Combine like terms: -36 + 110.25 = 74.25 110.25 + -21x + x2 = 74.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 74.25 Calculate the square root of the right side: 8.61684397 Break this problem into two subproblems by setting (x + -10.5) equal to 8.61684397 and -8.61684397.Subproblem 1
x + -10.5 = 8.61684397 Simplifying x + -10.5 = 8.61684397 Reorder the terms: -10.5 + x = 8.61684397 Solving -10.5 + x = 8.61684397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 8.61684397 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 8.61684397 + 10.5 x = 8.61684397 + 10.5 Combine like terms: 8.61684397 + 10.5 = 19.11684397 x = 19.11684397 Simplifying x = 19.11684397Subproblem 2
x + -10.5 = -8.61684397 Simplifying x + -10.5 = -8.61684397 Reorder the terms: -10.5 + x = -8.61684397 Solving -10.5 + x = -8.61684397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -8.61684397 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -8.61684397 + 10.5 x = -8.61684397 + 10.5 Combine like terms: -8.61684397 + 10.5 = 1.88315603 x = 1.88315603 Simplifying x = 1.88315603Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.11684397, 1.88315603}Solution
x = {19.11684397, 1.88315603}
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