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Simplifying 15x2 + -105x + 168 = 0 Reorder the terms: 168 + -105x + 15x2 = 0 Solving 168 + -105x + 15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(56 + -35x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(56 + -35x + 5x2)' equal to zero and attempt to solve: Simplifying 56 + -35x + 5x2 = 0 Solving 56 + -35x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 11.2 + -7x + x2 = 0 Move the constant term to the right: Add '-11.2' to each side of the equation. 11.2 + -7x + -11.2 + x2 = 0 + -11.2 Reorder the terms: 11.2 + -11.2 + -7x + x2 = 0 + -11.2 Combine like terms: 11.2 + -11.2 = 0.0 0.0 + -7x + x2 = 0 + -11.2 -7x + x2 = 0 + -11.2 Combine like terms: 0 + -11.2 = -11.2 -7x + x2 = -11.2 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 = -11.2 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -11.2 + 12.25 Combine like terms: -11.2 + 12.25 = 1.05 12.25 + -7x + x2 = 1.05 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 1.05 Calculate the square root of the right side: 1.024695077 Break this problem into two subproblems by setting (x + -3.5) equal to 1.024695077 and -1.024695077.Subproblem 1
x + -3.5 = 1.024695077 Simplifying x + -3.5 = 1.024695077 Reorder the terms: -3.5 + x = 1.024695077 Solving -3.5 + x = 1.024695077 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 = 1.024695077 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 1.024695077 + 3.5 x = 1.024695077 + 3.5 Combine like terms: 1.024695077 + 3.5 = 4.524695077 x = 4.524695077 Simplifying x = 4.524695077Subproblem 2
x + -3.5 = -1.024695077 Simplifying x + -3.5 = -1.024695077 Reorder the terms: -3.5 + x = -1.024695077 Solving -3.5 + x = -1.024695077 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 = -1.024695077 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -1.024695077 + 3.5 x = -1.024695077 + 3.5 Combine like terms: -1.024695077 + 3.5 = 2.475304923 x = 2.475304923 Simplifying x = 2.475304923Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.524695077, 2.475304923}Solution
x = {4.524695077, 2.475304923}
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