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Simplifying 4x2 + -56x + 42 = 0 Reorder the terms: 42 + -56x + 4x2 = 0 Solving 42 + -56x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + -28x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(21 + -28x + 2x2)' equal to zero and attempt to solve: Simplifying 21 + -28x + 2x2 = 0 Solving 21 + -28x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10.5 + -14x + x2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + -14x + -10.5 + x2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + -14x + x2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + -14x + x2 = 0 + -10.5 -14x + x2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 -14x + x2 = -10.5 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 = -10.5 + 49 Reorder the terms: 49 + -14x + x2 = -10.5 + 49 Combine like terms: -10.5 + 49 = 38.5 49 + -14x + x2 = 38.5 Factor a perfect square on the left side: (x + -7)(x + -7) = 38.5 Calculate the square root of the right side: 6.204836823 Break this problem into two subproblems by setting (x + -7) equal to 6.204836823 and -6.204836823.Subproblem 1
x + -7 = 6.204836823 Simplifying x + -7 = 6.204836823 Reorder the terms: -7 + x = 6.204836823 Solving -7 + x = 6.204836823 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 = 6.204836823 + 7 Combine like terms: -7 + 7 = 0 0 + x = 6.204836823 + 7 x = 6.204836823 + 7 Combine like terms: 6.204836823 + 7 = 13.204836823 x = 13.204836823 Simplifying x = 13.204836823Subproblem 2
x + -7 = -6.204836823 Simplifying x + -7 = -6.204836823 Reorder the terms: -7 + x = -6.204836823 Solving -7 + x = -6.204836823 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 = -6.204836823 + 7 Combine like terms: -7 + 7 = 0 0 + x = -6.204836823 + 7 x = -6.204836823 + 7 Combine like terms: -6.204836823 + 7 = 0.795163177 x = 0.795163177 Simplifying x = 0.795163177Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.204836823, 0.795163177}Solution
x = {13.204836823, 0.795163177}
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