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Simplifying 105x2 + -9x + -120 = 0 Reorder the terms: -120 + -9x + 105x2 = 0 Solving -120 + -9x + 105x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-40 + -3x + 35x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-40 + -3x + 35x2)' equal to zero and attempt to solve: Simplifying -40 + -3x + 35x2 = 0 Solving -40 + -3x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -1.142857143 + -0.08571428571x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + -0.08571428571x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + -0.08571428571x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + -0.08571428571x + x2 = 0 + 1.142857143 -0.08571428571x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 -0.08571428571x + x2 = 1.142857143 The x term is -0.08571428571x. Take half its coefficient (-0.04285714286). Square it (0.001836734694) and add it to both sides. Add '0.001836734694' to each side of the equation. -0.08571428571x + 0.001836734694 + x2 = 1.142857143 + 0.001836734694 Reorder the terms: 0.001836734694 + -0.08571428571x + x2 = 1.142857143 + 0.001836734694 Combine like terms: 1.142857143 + 0.001836734694 = 1.144693877694 0.001836734694 + -0.08571428571x + x2 = 1.144693877694 Factor a perfect square on the left side: (x + -0.04285714286)(x + -0.04285714286) = 1.144693877694 Calculate the square root of the right side: 1.069903677 Break this problem into two subproblems by setting (x + -0.04285714286) equal to 1.069903677 and -1.069903677.Subproblem 1
x + -0.04285714286 = 1.069903677 Simplifying x + -0.04285714286 = 1.069903677 Reorder the terms: -0.04285714286 + x = 1.069903677 Solving -0.04285714286 + x = 1.069903677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04285714286' to each side of the equation. -0.04285714286 + 0.04285714286 + x = 1.069903677 + 0.04285714286 Combine like terms: -0.04285714286 + 0.04285714286 = 0.00000000000 0.00000000000 + x = 1.069903677 + 0.04285714286 x = 1.069903677 + 0.04285714286 Combine like terms: 1.069903677 + 0.04285714286 = 1.11276081986 x = 1.11276081986 Simplifying x = 1.11276081986Subproblem 2
x + -0.04285714286 = -1.069903677 Simplifying x + -0.04285714286 = -1.069903677 Reorder the terms: -0.04285714286 + x = -1.069903677 Solving -0.04285714286 + x = -1.069903677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04285714286' to each side of the equation. -0.04285714286 + 0.04285714286 + x = -1.069903677 + 0.04285714286 Combine like terms: -0.04285714286 + 0.04285714286 = 0.00000000000 0.00000000000 + x = -1.069903677 + 0.04285714286 x = -1.069903677 + 0.04285714286 Combine like terms: -1.069903677 + 0.04285714286 = -1.02704653414 x = -1.02704653414 Simplifying x = -1.02704653414Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.11276081986, -1.02704653414}Solution
x = {1.11276081986, -1.02704653414}
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