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Simplifying 0 = x2 + -21x + 24 Reorder the terms: 0 = 24 + -21x + x2 Solving 0 = 24 + -21x + x2 Solving for variable 'x'. Combine like terms: 0 + -24 = -24 -24 + 21x + -1x2 = 24 + -21x + x2 + -24 + 21x + -1x2 Reorder the terms: -24 + 21x + -1x2 = 24 + -24 + -21x + 21x + x2 + -1x2 Combine like terms: 24 + -24 = 0 -24 + 21x + -1x2 = 0 + -21x + 21x + x2 + -1x2 -24 + 21x + -1x2 = -21x + 21x + x2 + -1x2 Combine like terms: -21x + 21x = 0 -24 + 21x + -1x2 = 0 + x2 + -1x2 -24 + 21x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -24 + 21x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 24 + -21x + x2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + -21x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -21x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -21x + x2 = 0 + -24 -21x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -21x + x2 = -24 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 = -24 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -24 + 110.25 Combine like terms: -24 + 110.25 = 86.25 110.25 + -21x + x2 = 86.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 86.25 Calculate the square root of the right side: 9.287087811 Break this problem into two subproblems by setting (x + -10.5) equal to 9.287087811 and -9.287087811.Subproblem 1
x + -10.5 = 9.287087811 Simplifying x + -10.5 = 9.287087811 Reorder the terms: -10.5 + x = 9.287087811 Solving -10.5 + x = 9.287087811 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 = 9.287087811 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 9.287087811 + 10.5 x = 9.287087811 + 10.5 Combine like terms: 9.287087811 + 10.5 = 19.787087811 x = 19.787087811 Simplifying x = 19.787087811Subproblem 2
x + -10.5 = -9.287087811 Simplifying x + -10.5 = -9.287087811 Reorder the terms: -10.5 + x = -9.287087811 Solving -10.5 + x = -9.287087811 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 = -9.287087811 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -9.287087811 + 10.5 x = -9.287087811 + 10.5 Combine like terms: -9.287087811 + 10.5 = 1.212912189 x = 1.212912189 Simplifying x = 1.212912189Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.787087811, 1.212912189}
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