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Simplifying 0 = 15x2 + -26x + -168 Reorder the terms: 0 = -168 + -26x + 15x2 Solving 0 = -168 + -26x + 15x2 Solving for variable 'x'. Combine like terms: 0 + 168 = 168 168 + 26x + -15x2 = -168 + -26x + 15x2 + 168 + 26x + -15x2 Reorder the terms: 168 + 26x + -15x2 = -168 + 168 + -26x + 26x + 15x2 + -15x2 Combine like terms: -168 + 168 = 0 168 + 26x + -15x2 = 0 + -26x + 26x + 15x2 + -15x2 168 + 26x + -15x2 = -26x + 26x + 15x2 + -15x2 Combine like terms: -26x + 26x = 0 168 + 26x + -15x2 = 0 + 15x2 + -15x2 168 + 26x + -15x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 168 + 26x + -15x2 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -11.2 + -1.733333333x + x2 = 0 Move the constant term to the right: Add '11.2' to each side of the equation. -11.2 + -1.733333333x + 11.2 + x2 = 0 + 11.2 Reorder the terms: -11.2 + 11.2 + -1.733333333x + x2 = 0 + 11.2 Combine like terms: -11.2 + 11.2 = 0.0 0.0 + -1.733333333x + x2 = 0 + 11.2 -1.733333333x + x2 = 0 + 11.2 Combine like terms: 0 + 11.2 = 11.2 -1.733333333x + x2 = 11.2 The x term is -1.733333333x. Take half its coefficient (-0.8666666665). Square it (0.7511111108) and add it to both sides. Add '0.7511111108' to each side of the equation. -1.733333333x + 0.7511111108 + x2 = 11.2 + 0.7511111108 Reorder the terms: 0.7511111108 + -1.733333333x + x2 = 11.2 + 0.7511111108 Combine like terms: 11.2 + 0.7511111108 = 11.9511111108 0.7511111108 + -1.733333333x + x2 = 11.9511111108 Factor a perfect square on the left side: (x + -0.8666666665)(x + -0.8666666665) = 11.9511111108 Calculate the square root of the right side: 3.45703791 Break this problem into two subproblems by setting (x + -0.8666666665) equal to 3.45703791 and -3.45703791.Subproblem 1
x + -0.8666666665 = 3.45703791 Simplifying x + -0.8666666665 = 3.45703791 Reorder the terms: -0.8666666665 + x = 3.45703791 Solving -0.8666666665 + x = 3.45703791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8666666665' to each side of the equation. -0.8666666665 + 0.8666666665 + x = 3.45703791 + 0.8666666665 Combine like terms: -0.8666666665 + 0.8666666665 = 0.0000000000 0.0000000000 + x = 3.45703791 + 0.8666666665 x = 3.45703791 + 0.8666666665 Combine like terms: 3.45703791 + 0.8666666665 = 4.3237045765 x = 4.3237045765 Simplifying x = 4.3237045765Subproblem 2
x + -0.8666666665 = -3.45703791 Simplifying x + -0.8666666665 = -3.45703791 Reorder the terms: -0.8666666665 + x = -3.45703791 Solving -0.8666666665 + x = -3.45703791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8666666665' to each side of the equation. -0.8666666665 + 0.8666666665 + x = -3.45703791 + 0.8666666665 Combine like terms: -0.8666666665 + 0.8666666665 = 0.0000000000 0.0000000000 + x = -3.45703791 + 0.8666666665 x = -3.45703791 + 0.8666666665 Combine like terms: -3.45703791 + 0.8666666665 = -2.5903712435 x = -2.5903712435 Simplifying x = -2.5903712435Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.3237045765, -2.5903712435}
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