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Simplifying 0 = 10x2 + 77x + 51 Reorder the terms: 0 = 51 + 77x + 10x2 Solving 0 = 51 + 77x + 10x2 Solving for variable 'x'. Combine like terms: 0 + -51 = -51 -51 + -77x + -10x2 = 51 + 77x + 10x2 + -51 + -77x + -10x2 Reorder the terms: -51 + -77x + -10x2 = 51 + -51 + 77x + -77x + 10x2 + -10x2 Combine like terms: 51 + -51 = 0 -51 + -77x + -10x2 = 0 + 77x + -77x + 10x2 + -10x2 -51 + -77x + -10x2 = 77x + -77x + 10x2 + -10x2 Combine like terms: 77x + -77x = 0 -51 + -77x + -10x2 = 0 + 10x2 + -10x2 -51 + -77x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -51 + -77x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(51 + 77x + 10x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(51 + 77x + 10x2)' equal to zero and attempt to solve: Simplifying 51 + 77x + 10x2 = 0 Solving 51 + 77x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 5.1 + 7.7x + x2 = 0.0 Move the constant term to the right: Add '-5.1' to each side of the equation. 5.1 + 7.7x + -5.1 + x2 = 0.0 + -5.1 Reorder the terms: 5.1 + -5.1 + 7.7x + x2 = 0.0 + -5.1 Combine like terms: 5.1 + -5.1 = 0.0 0.0 + 7.7x + x2 = 0.0 + -5.1 7.7x + x2 = 0.0 + -5.1 Combine like terms: 0.0 + -5.1 = -5.1 7.7x + x2 = -5.1 The x term is 7.7x. Take half its coefficient (3.85). Square it (14.8225) and add it to both sides. Add '14.8225' to each side of the equation. 7.7x + 14.8225 + x2 = -5.1 + 14.8225 Reorder the terms: 14.8225 + 7.7x + x2 = -5.1 + 14.8225 Combine like terms: -5.1 + 14.8225 = 9.7225 14.8225 + 7.7x + x2 = 9.7225 Factor a perfect square on the left side: (x + 3.85)(x + 3.85) = 9.7225 Calculate the square root of the right side: 3.118092366 Break this problem into two subproblems by setting (x + 3.85) equal to 3.118092366 and -3.118092366.Subproblem 1
x + 3.85 = 3.118092366 Simplifying x + 3.85 = 3.118092366 Reorder the terms: 3.85 + x = 3.118092366 Solving 3.85 + x = 3.118092366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.85' to each side of the equation. 3.85 + -3.85 + x = 3.118092366 + -3.85 Combine like terms: 3.85 + -3.85 = 0.00 0.00 + x = 3.118092366 + -3.85 x = 3.118092366 + -3.85 Combine like terms: 3.118092366 + -3.85 = -0.731907634 x = -0.731907634 Simplifying x = -0.731907634Subproblem 2
x + 3.85 = -3.118092366 Simplifying x + 3.85 = -3.118092366 Reorder the terms: 3.85 + x = -3.118092366 Solving 3.85 + x = -3.118092366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.85' to each side of the equation. 3.85 + -3.85 + x = -3.118092366 + -3.85 Combine like terms: 3.85 + -3.85 = 0.00 0.00 + x = -3.118092366 + -3.85 x = -3.118092366 + -3.85 Combine like terms: -3.118092366 + -3.85 = -6.968092366 x = -6.968092366 Simplifying x = -6.968092366Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.731907634, -6.968092366}Solution
x = {-0.731907634, -6.968092366}
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