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Simplifying 18x2 + 84x + -5790 = 0 Reorder the terms: -5790 + 84x + 18x2 = 0 Solving -5790 + 84x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-965 + 14x + 3x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-965 + 14x + 3x2)' equal to zero and attempt to solve: Simplifying -965 + 14x + 3x2 = 0 Solving -965 + 14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -321.6666667 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '321.6666667' to each side of the equation. -321.6666667 + 4.666666667x + 321.6666667 + x2 = 0 + 321.6666667 Reorder the terms: -321.6666667 + 321.6666667 + 4.666666667x + x2 = 0 + 321.6666667 Combine like terms: -321.6666667 + 321.6666667 = 0.0000000 0.0000000 + 4.666666667x + x2 = 0 + 321.6666667 4.666666667x + x2 = 0 + 321.6666667 Combine like terms: 0 + 321.6666667 = 321.6666667 4.666666667x + x2 = 321.6666667 The x term is 4.666666667x. Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. 4.666666667x + 5.444444448 + x2 = 321.6666667 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = 321.6666667 + 5.444444448 Combine like terms: 321.6666667 + 5.444444448 = 327.111111148 5.444444448 + 4.666666667x + x2 = 327.111111148 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = 327.111111148 Calculate the square root of the right side: 18.086213289 Break this problem into two subproblems by setting (x + 2.333333334) equal to 18.086213289 and -18.086213289.Subproblem 1
x + 2.333333334 = 18.086213289 Simplifying x + 2.333333334 = 18.086213289 Reorder the terms: 2.333333334 + x = 18.086213289 Solving 2.333333334 + x = 18.086213289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = 18.086213289 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 18.086213289 + -2.333333334 x = 18.086213289 + -2.333333334 Combine like terms: 18.086213289 + -2.333333334 = 15.752879955 x = 15.752879955 Simplifying x = 15.752879955Subproblem 2
x + 2.333333334 = -18.086213289 Simplifying x + 2.333333334 = -18.086213289 Reorder the terms: 2.333333334 + x = -18.086213289 Solving 2.333333334 + x = -18.086213289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = -18.086213289 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -18.086213289 + -2.333333334 x = -18.086213289 + -2.333333334 Combine like terms: -18.086213289 + -2.333333334 = -20.419546623 x = -20.419546623 Simplifying x = -20.419546623Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.752879955, -20.419546623}Solution
x = {15.752879955, -20.419546623}
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