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Simplifying 72x + -26x2 + -27 = 0 Reorder the terms: -27 + 72x + -26x2 = 0 Solving -27 + 72x + -26x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -26 the coefficient of the squared term: Divide each side by '-26'. 1.038461538 + -2.769230769x + x2 = 0 Move the constant term to the right: Add '-1.038461538' to each side of the equation. 1.038461538 + -2.769230769x + -1.038461538 + x2 = 0 + -1.038461538 Reorder the terms: 1.038461538 + -1.038461538 + -2.769230769x + x2 = 0 + -1.038461538 Combine like terms: 1.038461538 + -1.038461538 = 0.000000000 0.000000000 + -2.769230769x + x2 = 0 + -1.038461538 -2.769230769x + x2 = 0 + -1.038461538 Combine like terms: 0 + -1.038461538 = -1.038461538 -2.769230769x + x2 = -1.038461538 The x term is -2.769230769x. Take half its coefficient (-1.384615385). Square it (1.917159764) and add it to both sides. Add '1.917159764' to each side of the equation. -2.769230769x + 1.917159764 + x2 = -1.038461538 + 1.917159764 Reorder the terms: 1.917159764 + -2.769230769x + x2 = -1.038461538 + 1.917159764 Combine like terms: -1.038461538 + 1.917159764 = 0.878698226 1.917159764 + -2.769230769x + x2 = 0.878698226 Factor a perfect square on the left side: (x + -1.384615385)(x + -1.384615385) = 0.878698226 Calculate the square root of the right side: 0.937389047 Break this problem into two subproblems by setting (x + -1.384615385) equal to 0.937389047 and -0.937389047.Subproblem 1
x + -1.384615385 = 0.937389047 Simplifying x + -1.384615385 = 0.937389047 Reorder the terms: -1.384615385 + x = 0.937389047 Solving -1.384615385 + x = 0.937389047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.384615385' to each side of the equation. -1.384615385 + 1.384615385 + x = 0.937389047 + 1.384615385 Combine like terms: -1.384615385 + 1.384615385 = 0.000000000 0.000000000 + x = 0.937389047 + 1.384615385 x = 0.937389047 + 1.384615385 Combine like terms: 0.937389047 + 1.384615385 = 2.322004432 x = 2.322004432 Simplifying x = 2.322004432Subproblem 2
x + -1.384615385 = -0.937389047 Simplifying x + -1.384615385 = -0.937389047 Reorder the terms: -1.384615385 + x = -0.937389047 Solving -1.384615385 + x = -0.937389047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.384615385' to each side of the equation. -1.384615385 + 1.384615385 + x = -0.937389047 + 1.384615385 Combine like terms: -1.384615385 + 1.384615385 = 0.000000000 0.000000000 + x = -0.937389047 + 1.384615385 x = -0.937389047 + 1.384615385 Combine like terms: -0.937389047 + 1.384615385 = 0.447226338 x = 0.447226338 Simplifying x = 0.447226338Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.322004432, 0.447226338}
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