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Simplifying 36x2 + -252x + -27 = 0 Reorder the terms: -27 + -252x + 36x2 = 0 Solving -27 + -252x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(-3 + -28x + 4x2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-3 + -28x + 4x2)' equal to zero and attempt to solve: Simplifying -3 + -28x + 4x2 = 0 Solving -3 + -28x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + -7x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -7x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -7x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -7x + x2 = 0 + 0.75 -7x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -7x + x2 = 0.75 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 0.75 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 0.75 + 12.25 Combine like terms: 0.75 + 12.25 = 13 12.25 + -7x + x2 = 13 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + -3.5) equal to 3.605551275 and -3.605551275.Subproblem 1
x + -3.5 = 3.605551275 Simplifying x + -3.5 = 3.605551275 Reorder the terms: -3.5 + x = 3.605551275 Solving -3.5 + x = 3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.605551275 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.605551275 + 3.5 x = 3.605551275 + 3.5 Combine like terms: 3.605551275 + 3.5 = 7.105551275 x = 7.105551275 Simplifying x = 7.105551275Subproblem 2
x + -3.5 = -3.605551275 Simplifying x + -3.5 = -3.605551275 Reorder the terms: -3.5 + x = -3.605551275 Solving -3.5 + x = -3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.605551275 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.605551275 + 3.5 x = -3.605551275 + 3.5 Combine like terms: -3.605551275 + 3.5 = -0.105551275 x = -0.105551275 Simplifying x = -0.105551275Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.105551275, -0.105551275}Solution
x = {7.105551275, -0.105551275}
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