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Simplifying 6x2 + -63x + 84 = 0 Reorder the terms: 84 + -63x + 6x2 = 0 Solving 84 + -63x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(28 + -21x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(28 + -21x + 2x2)' equal to zero and attempt to solve: Simplifying 28 + -21x + 2x2 = 0 Solving 28 + -21x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 14 + -10.5x + x2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + -10.5x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -10.5x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -10.5x + x2 = 0 + -14 -10.5x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -10.5x + x2 = -14 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 = -14 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = -14 + 27.5625 Combine like terms: -14 + 27.5625 = 13.5625 27.5625 + -10.5x + x2 = 13.5625 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (x + -5.25) equal to 3.682729966 and -3.682729966.Subproblem 1
x + -5.25 = 3.682729966 Simplifying x + -5.25 = 3.682729966 Reorder the terms: -5.25 + x = 3.682729966 Solving -5.25 + x = 3.682729966 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 = 3.682729966 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 3.682729966 + 5.25 x = 3.682729966 + 5.25 Combine like terms: 3.682729966 + 5.25 = 8.932729966 x = 8.932729966 Simplifying x = 8.932729966Subproblem 2
x + -5.25 = -3.682729966 Simplifying x + -5.25 = -3.682729966 Reorder the terms: -5.25 + x = -3.682729966 Solving -5.25 + x = -3.682729966 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 = -3.682729966 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -3.682729966 + 5.25 x = -3.682729966 + 5.25 Combine like terms: -3.682729966 + 5.25 = 1.567270034 x = 1.567270034 Simplifying x = 1.567270034Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.932729966, 1.567270034}Solution
x = {8.932729966, 1.567270034}
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