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Simplifying -10x2 + -42x + 330 = 0 Reorder the terms: 330 + -42x + -10x2 = 0 Solving 330 + -42x + -10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(165 + -21x + -5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(165 + -21x + -5x2)' equal to zero and attempt to solve: Simplifying 165 + -21x + -5x2 = 0 Solving 165 + -21x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -33 + 4.2x + x2 = 0 Move the constant term to the right: Add '33' to each side of the equation. -33 + 4.2x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + 4.2x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 4.2x + x2 = 0 + 33 4.2x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 4.2x + x2 = 33 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 = 33 + 4.41 Reorder the terms: 4.41 + 4.2x + x2 = 33 + 4.41 Combine like terms: 33 + 4.41 = 37.41 4.41 + 4.2x + x2 = 37.41 Factor a perfect square on the left side: (x + 2.1)(x + 2.1) = 37.41 Calculate the square root of the right side: 6.116371473 Break this problem into two subproblems by setting (x + 2.1) equal to 6.116371473 and -6.116371473.Subproblem 1
x + 2.1 = 6.116371473 Simplifying x + 2.1 = 6.116371473 Reorder the terms: 2.1 + x = 6.116371473 Solving 2.1 + x = 6.116371473 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 = 6.116371473 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = 6.116371473 + -2.1 x = 6.116371473 + -2.1 Combine like terms: 6.116371473 + -2.1 = 4.016371473 x = 4.016371473 Simplifying x = 4.016371473Subproblem 2
x + 2.1 = -6.116371473 Simplifying x + 2.1 = -6.116371473 Reorder the terms: 2.1 + x = -6.116371473 Solving 2.1 + x = -6.116371473 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 = -6.116371473 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = -6.116371473 + -2.1 x = -6.116371473 + -2.1 Combine like terms: -6.116371473 + -2.1 = -8.216371473 x = -8.216371473 Simplifying x = -8.216371473Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.016371473, -8.216371473}Solution
x = {4.016371473, -8.216371473}
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