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Simplifying 21x2 + 75x + -120 = 0 Reorder the terms: -120 + 75x + 21x2 = 0 Solving -120 + 75x + 21x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-40 + 25x + 7x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-40 + 25x + 7x2)' equal to zero and attempt to solve: Simplifying -40 + 25x + 7x2 = 0 Solving -40 + 25x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5.714285714 + 3.571428571x + x2 = 0 Move the constant term to the right: Add '5.714285714' to each side of the equation. -5.714285714 + 3.571428571x + 5.714285714 + x2 = 0 + 5.714285714 Reorder the terms: -5.714285714 + 5.714285714 + 3.571428571x + x2 = 0 + 5.714285714 Combine like terms: -5.714285714 + 5.714285714 = 0.000000000 0.000000000 + 3.571428571x + x2 = 0 + 5.714285714 3.571428571x + x2 = 0 + 5.714285714 Combine like terms: 0 + 5.714285714 = 5.714285714 3.571428571x + x2 = 5.714285714 The x term is 3.571428571x. Take half its coefficient (1.785714286). Square it (3.188775511) and add it to both sides. Add '3.188775511' to each side of the equation. 3.571428571x + 3.188775511 + x2 = 5.714285714 + 3.188775511 Reorder the terms: 3.188775511 + 3.571428571x + x2 = 5.714285714 + 3.188775511 Combine like terms: 5.714285714 + 3.188775511 = 8.903061225 3.188775511 + 3.571428571x + x2 = 8.903061225 Factor a perfect square on the left side: (x + 1.785714286)(x + 1.785714286) = 8.903061225 Calculate the square root of the right side: 2.983799796 Break this problem into two subproblems by setting (x + 1.785714286) equal to 2.983799796 and -2.983799796.Subproblem 1
x + 1.785714286 = 2.983799796 Simplifying x + 1.785714286 = 2.983799796 Reorder the terms: 1.785714286 + x = 2.983799796 Solving 1.785714286 + x = 2.983799796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.785714286' to each side of the equation. 1.785714286 + -1.785714286 + x = 2.983799796 + -1.785714286 Combine like terms: 1.785714286 + -1.785714286 = 0.000000000 0.000000000 + x = 2.983799796 + -1.785714286 x = 2.983799796 + -1.785714286 Combine like terms: 2.983799796 + -1.785714286 = 1.19808551 x = 1.19808551 Simplifying x = 1.19808551Subproblem 2
x + 1.785714286 = -2.983799796 Simplifying x + 1.785714286 = -2.983799796 Reorder the terms: 1.785714286 + x = -2.983799796 Solving 1.785714286 + x = -2.983799796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.785714286' to each side of the equation. 1.785714286 + -1.785714286 + x = -2.983799796 + -1.785714286 Combine like terms: 1.785714286 + -1.785714286 = 0.000000000 0.000000000 + x = -2.983799796 + -1.785714286 x = -2.983799796 + -1.785714286 Combine like terms: -2.983799796 + -1.785714286 = -4.769514082 x = -4.769514082 Simplifying x = -4.769514082Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.19808551, -4.769514082}Solution
x = {1.19808551, -4.769514082}
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