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Simplifying 3x2 + x + -14 = 48 Reorder the terms: -14 + x + 3x2 = 48 Solving -14 + x + 3x2 = 48 Solving for variable 'x'. Reorder the terms: -14 + -48 + x + 3x2 = 48 + -48 Combine like terms: -14 + -48 = -62 -62 + x + 3x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -62 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -20.66666667 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '20.66666667' to each side of the equation. -20.66666667 + 0.3333333333x + 20.66666667 + x2 = 0 + 20.66666667 Reorder the terms: -20.66666667 + 20.66666667 + 0.3333333333x + x2 = 0 + 20.66666667 Combine like terms: -20.66666667 + 20.66666667 = 0.00000000 0.00000000 + 0.3333333333x + x2 = 0 + 20.66666667 0.3333333333x + x2 = 0 + 20.66666667 Combine like terms: 0 + 20.66666667 = 20.66666667 0.3333333333x + x2 = 20.66666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = 20.66666667 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = 20.66666667 + 0.25 Combine like terms: 20.66666667 + 0.25 = 20.91666667 0.25 + 0.3333333333x + x2 = 20.91666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 20.91666667 Calculate the square root of the right side: 4.573474245 Break this problem into two subproblems by setting (x + 0.5) equal to 4.573474245 and -4.573474245.Subproblem 1
x + 0.5 = 4.573474245 Simplifying x + 0.5 = 4.573474245 Reorder the terms: 0.5 + x = 4.573474245 Solving 0.5 + x = 4.573474245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.573474245 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.573474245 + -0.5 x = 4.573474245 + -0.5 Combine like terms: 4.573474245 + -0.5 = 4.073474245 x = 4.073474245 Simplifying x = 4.073474245Subproblem 2
x + 0.5 = -4.573474245 Simplifying x + 0.5 = -4.573474245 Reorder the terms: 0.5 + x = -4.573474245 Solving 0.5 + x = -4.573474245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.573474245 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.573474245 + -0.5 x = -4.573474245 + -0.5 Combine like terms: -4.573474245 + -0.5 = -5.073474245 x = -5.073474245 Simplifying x = -5.073474245Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.073474245, -5.073474245}
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