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Simplifying 4x2 + -78x + 168 = 0 Reorder the terms: 168 + -78x + 4x2 = 0 Solving 168 + -78x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(84 + -39x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(84 + -39x + 2x2)' equal to zero and attempt to solve: Simplifying 84 + -39x + 2x2 = 0 Solving 84 + -39x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 42 + -19.5x + x2 = 0 Move the constant term to the right: Add '-42' to each side of the equation. 42 + -19.5x + -42 + x2 = 0 + -42 Reorder the terms: 42 + -42 + -19.5x + x2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + -19.5x + x2 = 0 + -42 -19.5x + x2 = 0 + -42 Combine like terms: 0 + -42 = -42 -19.5x + x2 = -42 The x term is -19.5x. Take half its coefficient (-9.75). Square it (95.0625) and add it to both sides. Add '95.0625' to each side of the equation. -19.5x + 95.0625 + x2 = -42 + 95.0625 Reorder the terms: 95.0625 + -19.5x + x2 = -42 + 95.0625 Combine like terms: -42 + 95.0625 = 53.0625 95.0625 + -19.5x + x2 = 53.0625 Factor a perfect square on the left side: (x + -9.75)(x + -9.75) = 53.0625 Calculate the square root of the right side: 7.284401142 Break this problem into two subproblems by setting (x + -9.75) equal to 7.284401142 and -7.284401142.Subproblem 1
x + -9.75 = 7.284401142 Simplifying x + -9.75 = 7.284401142 Reorder the terms: -9.75 + x = 7.284401142 Solving -9.75 + x = 7.284401142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.75' to each side of the equation. -9.75 + 9.75 + x = 7.284401142 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + x = 7.284401142 + 9.75 x = 7.284401142 + 9.75 Combine like terms: 7.284401142 + 9.75 = 17.034401142 x = 17.034401142 Simplifying x = 17.034401142Subproblem 2
x + -9.75 = -7.284401142 Simplifying x + -9.75 = -7.284401142 Reorder the terms: -9.75 + x = -7.284401142 Solving -9.75 + x = -7.284401142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.75' to each side of the equation. -9.75 + 9.75 + x = -7.284401142 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + x = -7.284401142 + 9.75 x = -7.284401142 + 9.75 Combine like terms: -7.284401142 + 9.75 = 2.465598858 x = 2.465598858 Simplifying x = 2.465598858Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.034401142, 2.465598858}Solution
x = {17.034401142, 2.465598858}
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