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Simplifying x(x + -21) = 18 Reorder the terms: x(-21 + x) = 18 (-21 * x + x * x) = 18 (-21x + x2) = 18 Solving -21x + x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + -21x + x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + -21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -21x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -21x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -21x + x2 = 0 + 18 -21x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -21x + x2 = 18 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = 18 + 110.25 Reorder the terms: 110.25 + -21x + x2 = 18 + 110.25 Combine like terms: 18 + 110.25 = 128.25 110.25 + -21x + x2 = 128.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 128.25 Calculate the square root of the right side: 11.324751653 Break this problem into two subproblems by setting (x + -10.5) equal to 11.324751653 and -11.324751653.Subproblem 1
x + -10.5 = 11.324751653 Simplifying x + -10.5 = 11.324751653 Reorder the terms: -10.5 + x = 11.324751653 Solving -10.5 + x = 11.324751653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 11.324751653 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 11.324751653 + 10.5 x = 11.324751653 + 10.5 Combine like terms: 11.324751653 + 10.5 = 21.824751653 x = 21.824751653 Simplifying x = 21.824751653Subproblem 2
x + -10.5 = -11.324751653 Simplifying x + -10.5 = -11.324751653 Reorder the terms: -10.5 + x = -11.324751653 Solving -10.5 + x = -11.324751653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -11.324751653 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -11.324751653 + 10.5 x = -11.324751653 + 10.5 Combine like terms: -11.324751653 + 10.5 = -0.824751653 x = -0.824751653 Simplifying x = -0.824751653Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.824751653, -0.824751653}
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