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Simplifying -18x + 42 = x2 + -24x + -81 Reorder the terms: 42 + -18x = x2 + -24x + -81 Reorder the terms: 42 + -18x = -81 + -24x + x2 Solving 42 + -18x = -81 + -24x + x2 Solving for variable 'x'. Reorder the terms: 42 + 81 + -18x + 24x + -1x2 = -81 + -24x + x2 + 81 + 24x + -1x2 Combine like terms: 42 + 81 = 123 123 + -18x + 24x + -1x2 = -81 + -24x + x2 + 81 + 24x + -1x2 Combine like terms: -18x + 24x = 6x 123 + 6x + -1x2 = -81 + -24x + x2 + 81 + 24x + -1x2 Reorder the terms: 123 + 6x + -1x2 = -81 + 81 + -24x + 24x + x2 + -1x2 Combine like terms: -81 + 81 = 0 123 + 6x + -1x2 = 0 + -24x + 24x + x2 + -1x2 123 + 6x + -1x2 = -24x + 24x + x2 + -1x2 Combine like terms: -24x + 24x = 0 123 + 6x + -1x2 = 0 + x2 + -1x2 123 + 6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 123 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -123 + -6x + x2 = 0 Move the constant term to the right: Add '123' to each side of the equation. -123 + -6x + 123 + x2 = 0 + 123 Reorder the terms: -123 + 123 + -6x + x2 = 0 + 123 Combine like terms: -123 + 123 = 0 0 + -6x + x2 = 0 + 123 -6x + x2 = 0 + 123 Combine like terms: 0 + 123 = 123 -6x + x2 = 123 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 123 + 9 Reorder the terms: 9 + -6x + x2 = 123 + 9 Combine like terms: 123 + 9 = 132 9 + -6x + x2 = 132 Factor a perfect square on the left side: (x + -3)(x + -3) = 132 Calculate the square root of the right side: 11.489125293 Break this problem into two subproblems by setting (x + -3) equal to 11.489125293 and -11.489125293.Subproblem 1
x + -3 = 11.489125293 Simplifying x + -3 = 11.489125293 Reorder the terms: -3 + x = 11.489125293 Solving -3 + x = 11.489125293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 11.489125293 + 3 Combine like terms: -3 + 3 = 0 0 + x = 11.489125293 + 3 x = 11.489125293 + 3 Combine like terms: 11.489125293 + 3 = 14.489125293 x = 14.489125293 Simplifying x = 14.489125293Subproblem 2
x + -3 = -11.489125293 Simplifying x + -3 = -11.489125293 Reorder the terms: -3 + x = -11.489125293 Solving -3 + x = -11.489125293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -11.489125293 + 3 Combine like terms: -3 + 3 = 0 0 + x = -11.489125293 + 3 x = -11.489125293 + 3 Combine like terms: -11.489125293 + 3 = -8.489125293 x = -8.489125293 Simplifying x = -8.489125293Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.489125293, -8.489125293}
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