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Simplifying -1x2 + 72x + 79 = 0 Reorder the terms: 79 + 72x + -1x2 = 0 Solving 79 + 72x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -79 + -72x + x2 = 0 Move the constant term to the right: Add '79' to each side of the equation. -79 + -72x + 79 + x2 = 0 + 79 Reorder the terms: -79 + 79 + -72x + x2 = 0 + 79 Combine like terms: -79 + 79 = 0 0 + -72x + x2 = 0 + 79 -72x + x2 = 0 + 79 Combine like terms: 0 + 79 = 79 -72x + x2 = 79 The x term is -72x. Take half its coefficient (-36). Square it (1296) and add it to both sides. Add '1296' to each side of the equation. -72x + 1296 + x2 = 79 + 1296 Reorder the terms: 1296 + -72x + x2 = 79 + 1296 Combine like terms: 79 + 1296 = 1375 1296 + -72x + x2 = 1375 Factor a perfect square on the left side: (x + -36)(x + -36) = 1375 Calculate the square root of the right side: 37.080992435 Break this problem into two subproblems by setting (x + -36) equal to 37.080992435 and -37.080992435.Subproblem 1
x + -36 = 37.080992435 Simplifying x + -36 = 37.080992435 Reorder the terms: -36 + x = 37.080992435 Solving -36 + x = 37.080992435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = 37.080992435 + 36 Combine like terms: -36 + 36 = 0 0 + x = 37.080992435 + 36 x = 37.080992435 + 36 Combine like terms: 37.080992435 + 36 = 73.080992435 x = 73.080992435 Simplifying x = 73.080992435Subproblem 2
x + -36 = -37.080992435 Simplifying x + -36 = -37.080992435 Reorder the terms: -36 + x = -37.080992435 Solving -36 + x = -37.080992435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = -37.080992435 + 36 Combine like terms: -36 + 36 = 0 0 + x = -37.080992435 + 36 x = -37.080992435 + 36 Combine like terms: -37.080992435 + 36 = -1.080992435 x = -1.080992435 Simplifying x = -1.080992435Solution
The solution to the problem is based on the solutions from the subproblems. x = {73.080992435, -1.080992435}
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