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Simplifying 12x2 + 7x + -21 = 0 Reorder the terms: -21 + 7x + 12x2 = 0 Solving -21 + 7x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.75 + 0.5833333333x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 0.5833333333x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 0.5833333333x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 0.5833333333x + x2 = 0 + 1.75 0.5833333333x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 0.5833333333x + x2 = 1.75 The x term is 0.5833333333x. Take half its coefficient (0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. 0.5833333333x + 0.08506944446 + x2 = 1.75 + 0.08506944446 Reorder the terms: 0.08506944446 + 0.5833333333x + x2 = 1.75 + 0.08506944446 Combine like terms: 1.75 + 0.08506944446 = 1.83506944446 0.08506944446 + 0.5833333333x + x2 = 1.83506944446 Factor a perfect square on the left side: (x + 0.2916666667)(x + 0.2916666667) = 1.83506944446 Calculate the square root of the right side: 1.354647351 Break this problem into two subproblems by setting (x + 0.2916666667) equal to 1.354647351 and -1.354647351.Subproblem 1
x + 0.2916666667 = 1.354647351 Simplifying x + 0.2916666667 = 1.354647351 Reorder the terms: 0.2916666667 + x = 1.354647351 Solving 0.2916666667 + x = 1.354647351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2916666667' to each side of the equation. 0.2916666667 + -0.2916666667 + x = 1.354647351 + -0.2916666667 Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000 0.0000000000 + x = 1.354647351 + -0.2916666667 x = 1.354647351 + -0.2916666667 Combine like terms: 1.354647351 + -0.2916666667 = 1.0629806843 x = 1.0629806843 Simplifying x = 1.0629806843Subproblem 2
x + 0.2916666667 = -1.354647351 Simplifying x + 0.2916666667 = -1.354647351 Reorder the terms: 0.2916666667 + x = -1.354647351 Solving 0.2916666667 + x = -1.354647351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2916666667' to each side of the equation. 0.2916666667 + -0.2916666667 + x = -1.354647351 + -0.2916666667 Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000 0.0000000000 + x = -1.354647351 + -0.2916666667 x = -1.354647351 + -0.2916666667 Combine like terms: -1.354647351 + -0.2916666667 = -1.6463140177 x = -1.6463140177 Simplifying x = -1.6463140177Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0629806843, -1.6463140177}
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