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Simplifying x2 + -153x + 720 = 0 Reorder the terms: 720 + -153x + x2 = 0 Solving 720 + -153x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-720' to each side of the equation. 720 + -153x + -720 + x2 = 0 + -720 Reorder the terms: 720 + -720 + -153x + x2 = 0 + -720 Combine like terms: 720 + -720 = 0 0 + -153x + x2 = 0 + -720 -153x + x2 = 0 + -720 Combine like terms: 0 + -720 = -720 -153x + x2 = -720 The x term is -153x. Take half its coefficient (-76.5). Square it (5852.25) and add it to both sides. Add '5852.25' to each side of the equation. -153x + 5852.25 + x2 = -720 + 5852.25 Reorder the terms: 5852.25 + -153x + x2 = -720 + 5852.25 Combine like terms: -720 + 5852.25 = 5132.25 5852.25 + -153x + x2 = 5132.25 Factor a perfect square on the left side: (x + -76.5)(x + -76.5) = 5132.25 Calculate the square root of the right side: 71.639723618 Break this problem into two subproblems by setting (x + -76.5) equal to 71.639723618 and -71.639723618.Subproblem 1
x + -76.5 = 71.639723618 Simplifying x + -76.5 = 71.639723618 Reorder the terms: -76.5 + x = 71.639723618 Solving -76.5 + x = 71.639723618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '76.5' to each side of the equation. -76.5 + 76.5 + x = 71.639723618 + 76.5 Combine like terms: -76.5 + 76.5 = 0.0 0.0 + x = 71.639723618 + 76.5 x = 71.639723618 + 76.5 Combine like terms: 71.639723618 + 76.5 = 148.139723618 x = 148.139723618 Simplifying x = 148.139723618Subproblem 2
x + -76.5 = -71.639723618 Simplifying x + -76.5 = -71.639723618 Reorder the terms: -76.5 + x = -71.639723618 Solving -76.5 + x = -71.639723618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '76.5' to each side of the equation. -76.5 + 76.5 + x = -71.639723618 + 76.5 Combine like terms: -76.5 + 76.5 = 0.0 0.0 + x = -71.639723618 + 76.5 x = -71.639723618 + 76.5 Combine like terms: -71.639723618 + 76.5 = 4.860276382 x = 4.860276382 Simplifying x = 4.860276382Solution
The solution to the problem is based on the solutions from the subproblems. x = {148.139723618, 4.860276382}
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