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Simplifying 5x + 21 = x2 + 3 Reorder the terms: 21 + 5x = x2 + 3 Reorder the terms: 21 + 5x = 3 + x2 Solving 21 + 5x = 3 + x2 Solving for variable 'x'. Reorder the terms: 21 + -3 + 5x + -1x2 = 3 + x2 + -3 + -1x2 Combine like terms: 21 + -3 = 18 18 + 5x + -1x2 = 3 + x2 + -3 + -1x2 Reorder the terms: 18 + 5x + -1x2 = 3 + -3 + x2 + -1x2 Combine like terms: 3 + -3 = 0 18 + 5x + -1x2 = 0 + x2 + -1x2 18 + 5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 18 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -18 + -5x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -5x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -5x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -5x + x2 = 0 + 18 -5x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -5x + x2 = 18 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 18 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 18 + 6.25 Combine like terms: 18 + 6.25 = 24.25 6.25 + -5x + x2 = 24.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (x + -2.5) equal to 4.924428901 and -4.924428901.Subproblem 1
x + -2.5 = 4.924428901 Simplifying x + -2.5 = 4.924428901 Reorder the terms: -2.5 + x = 4.924428901 Solving -2.5 + x = 4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 4.924428901 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 4.924428901 + 2.5 x = 4.924428901 + 2.5 Combine like terms: 4.924428901 + 2.5 = 7.424428901 x = 7.424428901 Simplifying x = 7.424428901Subproblem 2
x + -2.5 = -4.924428901 Simplifying x + -2.5 = -4.924428901 Reorder the terms: -2.5 + x = -4.924428901 Solving -2.5 + x = -4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -4.924428901 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -4.924428901 + 2.5 x = -4.924428901 + 2.5 Combine like terms: -4.924428901 + 2.5 = -2.424428901 x = -2.424428901 Simplifying x = -2.424428901Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.424428901, -2.424428901}
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