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Simplifying 216 = (45 + x) * x Reorder the terms for easier multiplication: 216 = x(45 + x) 216 = (45 * x + x * x) 216 = (45x + x2) Solving 216 = 45x + x2 Solving for variable 'x'. Reorder the terms: 216 + -45x + -1x2 = 45x + -45x + x2 + -1x2 Combine like terms: 45x + -45x = 0 216 + -45x + -1x2 = 0 + x2 + -1x2 216 + -45x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 216 + -45x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -216 + 45x + x2 = 0 Move the constant term to the right: Add '216' to each side of the equation. -216 + 45x + 216 + x2 = 0 + 216 Reorder the terms: -216 + 216 + 45x + x2 = 0 + 216 Combine like terms: -216 + 216 = 0 0 + 45x + x2 = 0 + 216 45x + x2 = 0 + 216 Combine like terms: 0 + 216 = 216 45x + x2 = 216 The x term is 45x. Take half its coefficient (22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. 45x + 506.25 + x2 = 216 + 506.25 Reorder the terms: 506.25 + 45x + x2 = 216 + 506.25 Combine like terms: 216 + 506.25 = 722.25 506.25 + 45x + x2 = 722.25 Factor a perfect square on the left side: (x + 22.5)(x + 22.5) = 722.25 Calculate the square root of the right side: 26.874709301 Break this problem into two subproblems by setting (x + 22.5) equal to 26.874709301 and -26.874709301.Subproblem 1
x + 22.5 = 26.874709301 Simplifying x + 22.5 = 26.874709301 Reorder the terms: 22.5 + x = 26.874709301 Solving 22.5 + x = 26.874709301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + x = 26.874709301 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = 26.874709301 + -22.5 x = 26.874709301 + -22.5 Combine like terms: 26.874709301 + -22.5 = 4.374709301 x = 4.374709301 Simplifying x = 4.374709301Subproblem 2
x + 22.5 = -26.874709301 Simplifying x + 22.5 = -26.874709301 Reorder the terms: 22.5 + x = -26.874709301 Solving 22.5 + x = -26.874709301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + x = -26.874709301 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = -26.874709301 + -22.5 x = -26.874709301 + -22.5 Combine like terms: -26.874709301 + -22.5 = -49.374709301 x = -49.374709301 Simplifying x = -49.374709301Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.374709301, -49.374709301}
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