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Simplifying -10x2 + 120x + 3300 = 0 Reorder the terms: 3300 + 120x + -10x2 = 0 Solving 3300 + 120x + -10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(330 + 12x + -1x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(330 + 12x + -1x2)' equal to zero and attempt to solve: Simplifying 330 + 12x + -1x2 = 0 Solving 330 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -330 + -12x + x2 = 0 Move the constant term to the right: Add '330' to each side of the equation. -330 + -12x + 330 + x2 = 0 + 330 Reorder the terms: -330 + 330 + -12x + x2 = 0 + 330 Combine like terms: -330 + 330 = 0 0 + -12x + x2 = 0 + 330 -12x + x2 = 0 + 330 Combine like terms: 0 + 330 = 330 -12x + x2 = 330 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 330 + 36 Reorder the terms: 36 + -12x + x2 = 330 + 36 Combine like terms: 330 + 36 = 366 36 + -12x + x2 = 366 Factor a perfect square on the left side: (x + -6)(x + -6) = 366 Calculate the square root of the right side: 19.13112647 Break this problem into two subproblems by setting (x + -6) equal to 19.13112647 and -19.13112647.Subproblem 1
x + -6 = 19.13112647 Simplifying x + -6 = 19.13112647 Reorder the terms: -6 + x = 19.13112647 Solving -6 + x = 19.13112647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 19.13112647 + 6 Combine like terms: -6 + 6 = 0 0 + x = 19.13112647 + 6 x = 19.13112647 + 6 Combine like terms: 19.13112647 + 6 = 25.13112647 x = 25.13112647 Simplifying x = 25.13112647Subproblem 2
x + -6 = -19.13112647 Simplifying x + -6 = -19.13112647 Reorder the terms: -6 + x = -19.13112647 Solving -6 + x = -19.13112647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -19.13112647 + 6 Combine like terms: -6 + 6 = 0 0 + x = -19.13112647 + 6 x = -19.13112647 + 6 Combine like terms: -19.13112647 + 6 = -13.13112647 x = -13.13112647 Simplifying x = -13.13112647Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.13112647, -13.13112647}Solution
x = {25.13112647, -13.13112647}
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