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Simplifying 6x2 + 63x + -63 = 0 Reorder the terms: -63 + 63x + 6x2 = 0 Solving -63 + 63x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-21 + 21x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-21 + 21x + 2x2)' equal to zero and attempt to solve: Simplifying -21 + 21x + 2x2 = 0 Solving -21 + 21x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.5 + 10.5x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + 10.5x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + 10.5x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + 10.5x + x2 = 0 + 10.5 10.5x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 10.5x + x2 = 10.5 The x term is 10.5x. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5x + 27.5625 + x2 = 10.5 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = 10.5 + 27.5625 Combine like terms: 10.5 + 27.5625 = 38.0625 27.5625 + 10.5x + x2 = 38.0625 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 38.0625 Calculate the square root of the right side: 6.16948134 Break this problem into two subproblems by setting (x + 5.25) equal to 6.16948134 and -6.16948134.Subproblem 1
x + 5.25 = 6.16948134 Simplifying x + 5.25 = 6.16948134 Reorder the terms: 5.25 + x = 6.16948134 Solving 5.25 + x = 6.16948134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 6.16948134 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 6.16948134 + -5.25 x = 6.16948134 + -5.25 Combine like terms: 6.16948134 + -5.25 = 0.91948134 x = 0.91948134 Simplifying x = 0.91948134Subproblem 2
x + 5.25 = -6.16948134 Simplifying x + 5.25 = -6.16948134 Reorder the terms: 5.25 + x = -6.16948134 Solving 5.25 + x = -6.16948134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -6.16948134 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -6.16948134 + -5.25 x = -6.16948134 + -5.25 Combine like terms: -6.16948134 + -5.25 = -11.41948134 x = -11.41948134 Simplifying x = -11.41948134Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.91948134, -11.41948134}Solution
x = {0.91948134, -11.41948134}
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