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Simplifying 3x2 + -42x + 42 = 0 Reorder the terms: 42 + -42x + 3x2 = 0 Solving 42 + -42x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(14 + -14x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(14 + -14x + x2)' equal to zero and attempt to solve: Simplifying 14 + -14x + x2 = 0 Solving 14 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -14x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -14x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -14x + x2 = 0 + -14 -14x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -14x + x2 = -14 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 = -14 + 49 Reorder the terms: 49 + -14x + x2 = -14 + 49 Combine like terms: -14 + 49 = 35 49 + -14x + x2 = 35 Factor a perfect square on the left side: (x + -7)(x + -7) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (x + -7) equal to 5.916079783 and -5.916079783.Subproblem 1
x + -7 = 5.916079783 Simplifying x + -7 = 5.916079783 Reorder the terms: -7 + x = 5.916079783 Solving -7 + x = 5.916079783 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 = 5.916079783 + 7 Combine like terms: -7 + 7 = 0 0 + x = 5.916079783 + 7 x = 5.916079783 + 7 Combine like terms: 5.916079783 + 7 = 12.916079783 x = 12.916079783 Simplifying x = 12.916079783Subproblem 2
x + -7 = -5.916079783 Simplifying x + -7 = -5.916079783 Reorder the terms: -7 + x = -5.916079783 Solving -7 + x = -5.916079783 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 = -5.916079783 + 7 Combine like terms: -7 + 7 = 0 0 + x = -5.916079783 + 7 x = -5.916079783 + 7 Combine like terms: -5.916079783 + 7 = 1.083920217 x = 1.083920217 Simplifying x = 1.083920217Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.916079783, 1.083920217}Solution
x = {12.916079783, 1.083920217}
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