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Simplifying 3x2 + -42x + 18 = 0 Reorder the terms: 18 + -42x + 3x2 = 0 Solving 18 + -42x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(6 + -14x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + -14x + x2)' equal to zero and attempt to solve: Simplifying 6 + -14x + x2 = 0 Solving 6 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -14x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -14x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -14x + x2 = 0 + -6 -14x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -14x + x2 = -6 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -6 + 49 Reorder the terms: 49 + -14x + x2 = -6 + 49 Combine like terms: -6 + 49 = 43 49 + -14x + x2 = 43 Factor a perfect square on the left side: (x + -7)(x + -7) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (x + -7) equal to 6.557438524 and -6.557438524.Subproblem 1
x + -7 = 6.557438524 Simplifying x + -7 = 6.557438524 Reorder the terms: -7 + x = 6.557438524 Solving -7 + x = 6.557438524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 6.557438524 + 7 Combine like terms: -7 + 7 = 0 0 + x = 6.557438524 + 7 x = 6.557438524 + 7 Combine like terms: 6.557438524 + 7 = 13.557438524 x = 13.557438524 Simplifying x = 13.557438524Subproblem 2
x + -7 = -6.557438524 Simplifying x + -7 = -6.557438524 Reorder the terms: -7 + x = -6.557438524 Solving -7 + x = -6.557438524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -6.557438524 + 7 Combine like terms: -7 + 7 = 0 0 + x = -6.557438524 + 7 x = -6.557438524 + 7 Combine like terms: -6.557438524 + 7 = 0.442561476 x = 0.442561476 Simplifying x = 0.442561476Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.557438524, 0.442561476}Solution
x = {13.557438524, 0.442561476}
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