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Simplifying 2x + 24 = 2x2 + 16x Reorder the terms: 24 + 2x = 2x2 + 16x Reorder the terms: 24 + 2x = 16x + 2x2 Solving 24 + 2x = 16x + 2x2 Solving for variable 'x'. Combine like terms: 2x + -16x = -14x 24 + -14x + -2x2 = 16x + 2x2 + -16x + -2x2 Reorder the terms: 24 + -14x + -2x2 = 16x + -16x + 2x2 + -2x2 Combine like terms: 16x + -16x = 0 24 + -14x + -2x2 = 0 + 2x2 + -2x2 24 + -14x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 24 + -14x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -7x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + -7x + -1x2)' equal to zero and attempt to solve: Simplifying 12 + -7x + -1x2 = 0 Solving 12 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12 + 7x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 7x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 7x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 7x + x2 = 0 + 12 7x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 7x + x2 = 12 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 12 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 12 + 12.25 Combine like terms: 12 + 12.25 = 24.25 12.25 + 7x + x2 = 24.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (x + 3.5) equal to 4.924428901 and -4.924428901.Subproblem 1
x + 3.5 = 4.924428901 Simplifying x + 3.5 = 4.924428901 Reorder the terms: 3.5 + x = 4.924428901 Solving 3.5 + x = 4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 4.924428901 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.924428901 + -3.5 x = 4.924428901 + -3.5 Combine like terms: 4.924428901 + -3.5 = 1.424428901 x = 1.424428901 Simplifying x = 1.424428901Subproblem 2
x + 3.5 = -4.924428901 Simplifying x + 3.5 = -4.924428901 Reorder the terms: 3.5 + x = -4.924428901 Solving 3.5 + x = -4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -4.924428901 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.924428901 + -3.5 x = -4.924428901 + -3.5 Combine like terms: -4.924428901 + -3.5 = -8.424428901 x = -8.424428901 Simplifying x = -8.424428901Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.424428901, -8.424428901}Solution
x = {1.424428901, -8.424428901}
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