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Simplifying 12x2 + 3x + 8 = 76 Reorder the terms: 8 + 3x + 12x2 = 76 Solving 8 + 3x + 12x2 = 76 Solving for variable 'x'. Reorder the terms: 8 + -76 + 3x + 12x2 = 76 + -76 Combine like terms: 8 + -76 = -68 -68 + 3x + 12x2 = 76 + -76 Combine like terms: 76 + -76 = 0 -68 + 3x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -5.666666667 + 0.25x + x2 = 0 Move the constant term to the right: Add '5.666666667' to each side of the equation. -5.666666667 + 0.25x + 5.666666667 + x2 = 0 + 5.666666667 Reorder the terms: -5.666666667 + 5.666666667 + 0.25x + x2 = 0 + 5.666666667 Combine like terms: -5.666666667 + 5.666666667 = 0.000000000 0.000000000 + 0.25x + x2 = 0 + 5.666666667 0.25x + x2 = 0 + 5.666666667 Combine like terms: 0 + 5.666666667 = 5.666666667 0.25x + x2 = 5.666666667 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 5.666666667 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 5.666666667 + 0.015625 Combine like terms: 5.666666667 + 0.015625 = 5.682291667 0.015625 + 0.25x + x2 = 5.682291667 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 5.682291667 Calculate the square root of the right side: 2.38375579 Break this problem into two subproblems by setting (x + 0.125) equal to 2.38375579 and -2.38375579.Subproblem 1
x + 0.125 = 2.38375579 Simplifying x + 0.125 = 2.38375579 Reorder the terms: 0.125 + x = 2.38375579 Solving 0.125 + x = 2.38375579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 2.38375579 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 2.38375579 + -0.125 x = 2.38375579 + -0.125 Combine like terms: 2.38375579 + -0.125 = 2.25875579 x = 2.25875579 Simplifying x = 2.25875579Subproblem 2
x + 0.125 = -2.38375579 Simplifying x + 0.125 = -2.38375579 Reorder the terms: 0.125 + x = -2.38375579 Solving 0.125 + x = -2.38375579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -2.38375579 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -2.38375579 + -0.125 x = -2.38375579 + -0.125 Combine like terms: -2.38375579 + -0.125 = -2.50875579 x = -2.50875579 Simplifying x = -2.50875579Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.25875579, -2.50875579}
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