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Simplifying -4x2 + 1320x + -19800 = 0 Reorder the terms: -19800 + 1320x + -4x2 = 0 Solving -19800 + 1320x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-4950 + 330x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4950 + 330x + -1x2)' equal to zero and attempt to solve: Simplifying -4950 + 330x + -1x2 = 0 Solving -4950 + 330x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4950 + -330x + x2 = 0 Move the constant term to the right: Add '-4950' to each side of the equation. 4950 + -330x + -4950 + x2 = 0 + -4950 Reorder the terms: 4950 + -4950 + -330x + x2 = 0 + -4950 Combine like terms: 4950 + -4950 = 0 0 + -330x + x2 = 0 + -4950 -330x + x2 = 0 + -4950 Combine like terms: 0 + -4950 = -4950 -330x + x2 = -4950 The x term is -330x. Take half its coefficient (-165). Square it (27225) and add it to both sides. Add '27225' to each side of the equation. -330x + 27225 + x2 = -4950 + 27225 Reorder the terms: 27225 + -330x + x2 = -4950 + 27225 Combine like terms: -4950 + 27225 = 22275 27225 + -330x + x2 = 22275 Factor a perfect square on the left side: (x + -165)(x + -165) = 22275 Calculate the square root of the right side: 149.248115566 Break this problem into two subproblems by setting (x + -165) equal to 149.248115566 and -149.248115566.Subproblem 1
x + -165 = 149.248115566 Simplifying x + -165 = 149.248115566 Reorder the terms: -165 + x = 149.248115566 Solving -165 + x = 149.248115566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '165' to each side of the equation. -165 + 165 + x = 149.248115566 + 165 Combine like terms: -165 + 165 = 0 0 + x = 149.248115566 + 165 x = 149.248115566 + 165 Combine like terms: 149.248115566 + 165 = 314.248115566 x = 314.248115566 Simplifying x = 314.248115566Subproblem 2
x + -165 = -149.248115566 Simplifying x + -165 = -149.248115566 Reorder the terms: -165 + x = -149.248115566 Solving -165 + x = -149.248115566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '165' to each side of the equation. -165 + 165 + x = -149.248115566 + 165 Combine like terms: -165 + 165 = 0 0 + x = -149.248115566 + 165 x = -149.248115566 + 165 Combine like terms: -149.248115566 + 165 = 15.751884434 x = 15.751884434 Simplifying x = 15.751884434Solution
The solution to the problem is based on the solutions from the subproblems. x = {314.248115566, 15.751884434}Solution
x = {314.248115566, 15.751884434}
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