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Simplifying 15x2 + -68x + 72 = 0 Reorder the terms: 72 + -68x + 15x2 = 0 Solving 72 + -68x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 4.8 + -4.533333333x + x2 = 0 Move the constant term to the right: Add '-4.8' to each side of the equation. 4.8 + -4.533333333x + -4.8 + x2 = 0 + -4.8 Reorder the terms: 4.8 + -4.8 + -4.533333333x + x2 = 0 + -4.8 Combine like terms: 4.8 + -4.8 = 0.0 0.0 + -4.533333333x + x2 = 0 + -4.8 -4.533333333x + x2 = 0 + -4.8 Combine like terms: 0 + -4.8 = -4.8 -4.533333333x + x2 = -4.8 The x term is -4.533333333x. Take half its coefficient (-2.266666667). Square it (5.137777779) and add it to both sides. Add '5.137777779' to each side of the equation. -4.533333333x + 5.137777779 + x2 = -4.8 + 5.137777779 Reorder the terms: 5.137777779 + -4.533333333x + x2 = -4.8 + 5.137777779 Combine like terms: -4.8 + 5.137777779 = 0.337777779 5.137777779 + -4.533333333x + x2 = 0.337777779 Factor a perfect square on the left side: (x + -2.266666667)(x + -2.266666667) = 0.337777779 Calculate the square root of the right side: 0.581186527 Break this problem into two subproblems by setting (x + -2.266666667) equal to 0.581186527 and -0.581186527.Subproblem 1
x + -2.266666667 = 0.581186527 Simplifying x + -2.266666667 = 0.581186527 Reorder the terms: -2.266666667 + x = 0.581186527 Solving -2.266666667 + x = 0.581186527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.266666667' to each side of the equation. -2.266666667 + 2.266666667 + x = 0.581186527 + 2.266666667 Combine like terms: -2.266666667 + 2.266666667 = 0.000000000 0.000000000 + x = 0.581186527 + 2.266666667 x = 0.581186527 + 2.266666667 Combine like terms: 0.581186527 + 2.266666667 = 2.847853194 x = 2.847853194 Simplifying x = 2.847853194Subproblem 2
x + -2.266666667 = -0.581186527 Simplifying x + -2.266666667 = -0.581186527 Reorder the terms: -2.266666667 + x = -0.581186527 Solving -2.266666667 + x = -0.581186527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.266666667' to each side of the equation. -2.266666667 + 2.266666667 + x = -0.581186527 + 2.266666667 Combine like terms: -2.266666667 + 2.266666667 = 0.000000000 0.000000000 + x = -0.581186527 + 2.266666667 x = -0.581186527 + 2.266666667 Combine like terms: -0.581186527 + 2.266666667 = 1.68548014 x = 1.68548014 Simplifying x = 1.68548014Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.847853194, 1.68548014}
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