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Simplifying 4x2 + -36x = -6 Reorder the terms: -36x + 4x2 = -6 Solving -36x + 4x2 = -6 Solving for variable 'x'. Reorder the terms: 6 + -36x + 4x2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + -36x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -18x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -18x + 2x2)' equal to zero and attempt to solve: Simplifying 3 + -18x + 2x2 = 0 Solving 3 + -18x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -9x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -9x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -9x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -9x + x2 = 0 + -1.5 -9x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -9x + x2 = -1.5 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -1.5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -1.5 + 20.25 Combine like terms: -1.5 + 20.25 = 18.75 20.25 + -9x + x2 = 18.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 18.75 Calculate the square root of the right side: 4.330127019 Break this problem into two subproblems by setting (x + -4.5) equal to 4.330127019 and -4.330127019.Subproblem 1
x + -4.5 = 4.330127019 Simplifying x + -4.5 = 4.330127019 Reorder the terms: -4.5 + x = 4.330127019 Solving -4.5 + x = 4.330127019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 4.330127019 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.330127019 + 4.5 x = 4.330127019 + 4.5 Combine like terms: 4.330127019 + 4.5 = 8.830127019 x = 8.830127019 Simplifying x = 8.830127019Subproblem 2
x + -4.5 = -4.330127019 Simplifying x + -4.5 = -4.330127019 Reorder the terms: -4.5 + x = -4.330127019 Solving -4.5 + x = -4.330127019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -4.330127019 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.330127019 + 4.5 x = -4.330127019 + 4.5 Combine like terms: -4.330127019 + 4.5 = 0.169872981 x = 0.169872981 Simplifying x = 0.169872981Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.830127019, 0.169872981}Solution
x = {8.830127019, 0.169872981}
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