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Simplifying 6x2 + 42x + -18 = 0 Reorder the terms: -18 + 42x + 6x2 = 0 Solving -18 + 42x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-3 + 7x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-3 + 7x + x2)' equal to zero and attempt to solve: Simplifying -3 + 7x + x2 = 0 Solving -3 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 7x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 7x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 7x + x2 = 0 + 3 7x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 7x + x2 = 3 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 = 3 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 3 + 12.25 Combine like terms: 3 + 12.25 = 15.25 12.25 + 7x + x2 = 15.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + 3.5) equal to 3.905124838 and -3.905124838.Subproblem 1
x + 3.5 = 3.905124838 Simplifying x + 3.5 = 3.905124838 Reorder the terms: 3.5 + x = 3.905124838 Solving 3.5 + x = 3.905124838 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 = 3.905124838 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.905124838 + -3.5 x = 3.905124838 + -3.5 Combine like terms: 3.905124838 + -3.5 = 0.405124838 x = 0.405124838 Simplifying x = 0.405124838Subproblem 2
x + 3.5 = -3.905124838 Simplifying x + 3.5 = -3.905124838 Reorder the terms: 3.5 + x = -3.905124838 Solving 3.5 + x = -3.905124838 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 = -3.905124838 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.905124838 + -3.5 x = -3.905124838 + -3.5 Combine like terms: -3.905124838 + -3.5 = -7.405124838 x = -7.405124838 Simplifying x = -7.405124838Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.405124838, -7.405124838}Solution
x = {0.405124838, -7.405124838}
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