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Simplifying 30x2 + -126x + 120 = 0 Reorder the terms: 120 + -126x + 30x2 = 0 Solving 120 + -126x + 30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(20 + -21x + 5x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(20 + -21x + 5x2)' equal to zero and attempt to solve: Simplifying 20 + -21x + 5x2 = 0 Solving 20 + -21x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4 + -4.2x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -4.2x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -4.2x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -4.2x + x2 = 0 + -4 -4.2x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -4.2x + x2 = -4 The x term is -4.2x. Take half its coefficient (-2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. -4.2x + 4.41 + x2 = -4 + 4.41 Reorder the terms: 4.41 + -4.2x + x2 = -4 + 4.41 Combine like terms: -4 + 4.41 = 0.41 4.41 + -4.2x + x2 = 0.41 Factor a perfect square on the left side: (x + -2.1)(x + -2.1) = 0.41 Calculate the square root of the right side: 0.640312424 Break this problem into two subproblems by setting (x + -2.1) equal to 0.640312424 and -0.640312424.Subproblem 1
x + -2.1 = 0.640312424 Simplifying x + -2.1 = 0.640312424 Reorder the terms: -2.1 + x = 0.640312424 Solving -2.1 + x = 0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + x = 0.640312424 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + x = 0.640312424 + 2.1 x = 0.640312424 + 2.1 Combine like terms: 0.640312424 + 2.1 = 2.740312424 x = 2.740312424 Simplifying x = 2.740312424Subproblem 2
x + -2.1 = -0.640312424 Simplifying x + -2.1 = -0.640312424 Reorder the terms: -2.1 + x = -0.640312424 Solving -2.1 + x = -0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + x = -0.640312424 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + x = -0.640312424 + 2.1 x = -0.640312424 + 2.1 Combine like terms: -0.640312424 + 2.1 = 1.459687576 x = 1.459687576 Simplifying x = 1.459687576Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.740312424, 1.459687576}Solution
x = {2.740312424, 1.459687576}
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