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Simplifying -1x2 + -23x + 432 = 0 Reorder the terms: 432 + -23x + -1x2 = 0 Solving 432 + -23x + -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'. -432 + 23x + x2 = 0 Move the constant term to the right: Add '432' to each side of the equation. -432 + 23x + 432 + x2 = 0 + 432 Reorder the terms: -432 + 432 + 23x + x2 = 0 + 432 Combine like terms: -432 + 432 = 0 0 + 23x + x2 = 0 + 432 23x + x2 = 0 + 432 Combine like terms: 0 + 432 = 432 23x + x2 = 432 The x term is 23x. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23x + 132.25 + x2 = 432 + 132.25 Reorder the terms: 132.25 + 23x + x2 = 432 + 132.25 Combine like terms: 432 + 132.25 = 564.25 132.25 + 23x + x2 = 564.25 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 564.25 Calculate the square root of the right side: 23.75394704 Break this problem into two subproblems by setting (x + 11.5) equal to 23.75394704 and -23.75394704.Subproblem 1
x + 11.5 = 23.75394704 Simplifying x + 11.5 = 23.75394704 Reorder the terms: 11.5 + x = 23.75394704 Solving 11.5 + x = 23.75394704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = 23.75394704 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 23.75394704 + -11.5 x = 23.75394704 + -11.5 Combine like terms: 23.75394704 + -11.5 = 12.25394704 x = 12.25394704 Simplifying x = 12.25394704Subproblem 2
x + 11.5 = -23.75394704 Simplifying x + 11.5 = -23.75394704 Reorder the terms: 11.5 + x = -23.75394704 Solving 11.5 + x = -23.75394704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = -23.75394704 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -23.75394704 + -11.5 x = -23.75394704 + -11.5 Combine like terms: -23.75394704 + -11.5 = -35.25394704 x = -35.25394704 Simplifying x = -35.25394704Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.25394704, -35.25394704}
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