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Simplifying 6x2 + 27x + -30 = 0 Reorder the terms: -30 + 27x + 6x2 = 0 Solving -30 + 27x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-10 + 9x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-10 + 9x + 2x2)' equal to zero and attempt to solve: Simplifying -10 + 9x + 2x2 = 0 Solving -10 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5 + 4.5x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 4.5x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 4.5x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 4.5x + x2 = 0 + 5 4.5x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 4.5x + x2 = 5 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 5 + 5.0625 Combine like terms: 5 + 5.0625 = 10.0625 5.0625 + 4.5x + x2 = 10.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (x + 2.25) equal to 3.172144385 and -3.172144385.Subproblem 1
x + 2.25 = 3.172144385 Simplifying x + 2.25 = 3.172144385 Reorder the terms: 2.25 + x = 3.172144385 Solving 2.25 + x = 3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 3.172144385 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 3.172144385 + -2.25 x = 3.172144385 + -2.25 Combine like terms: 3.172144385 + -2.25 = 0.922144385 x = 0.922144385 Simplifying x = 0.922144385Subproblem 2
x + 2.25 = -3.172144385 Simplifying x + 2.25 = -3.172144385 Reorder the terms: 2.25 + x = -3.172144385 Solving 2.25 + x = -3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -3.172144385 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -3.172144385 + -2.25 x = -3.172144385 + -2.25 Combine like terms: -3.172144385 + -2.25 = -5.422144385 x = -5.422144385 Simplifying x = -5.422144385Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.922144385, -5.422144385}Solution
x = {0.922144385, -5.422144385}
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