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Simplifying -7x2 + -55x + -8 = 0 Reorder the terms: -8 + -55x + -7x2 = 0 Solving -8 + -55x + -7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 55x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 55x + 7x2)' equal to zero and attempt to solve: Simplifying 8 + 55x + 7x2 = 0 Solving 8 + 55x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.142857143 + 7.857142857x + x2 = 0 Move the constant term to the right: Add '-1.142857143' to each side of the equation. 1.142857143 + 7.857142857x + -1.142857143 + x2 = 0 + -1.142857143 Reorder the terms: 1.142857143 + -1.142857143 + 7.857142857x + x2 = 0 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + 7.857142857x + x2 = 0 + -1.142857143 7.857142857x + x2 = 0 + -1.142857143 Combine like terms: 0 + -1.142857143 = -1.142857143 7.857142857x + x2 = -1.142857143 The x term is 7.857142857x. Take half its coefficient (3.928571429). Square it (15.43367347) and add it to both sides. Add '15.43367347' to each side of the equation. 7.857142857x + 15.43367347 + x2 = -1.142857143 + 15.43367347 Reorder the terms: 15.43367347 + 7.857142857x + x2 = -1.142857143 + 15.43367347 Combine like terms: -1.142857143 + 15.43367347 = 14.290816327 15.43367347 + 7.857142857x + x2 = 14.290816327 Factor a perfect square on the left side: (x + 3.928571429)(x + 3.928571429) = 14.290816327 Calculate the square root of the right side: 3.780319606 Break this problem into two subproblems by setting (x + 3.928571429) equal to 3.780319606 and -3.780319606.Subproblem 1
x + 3.928571429 = 3.780319606 Simplifying x + 3.928571429 = 3.780319606 Reorder the terms: 3.928571429 + x = 3.780319606 Solving 3.928571429 + x = 3.780319606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.928571429' to each side of the equation. 3.928571429 + -3.928571429 + x = 3.780319606 + -3.928571429 Combine like terms: 3.928571429 + -3.928571429 = 0.000000000 0.000000000 + x = 3.780319606 + -3.928571429 x = 3.780319606 + -3.928571429 Combine like terms: 3.780319606 + -3.928571429 = -0.148251823 x = -0.148251823 Simplifying x = -0.148251823Subproblem 2
x + 3.928571429 = -3.780319606 Simplifying x + 3.928571429 = -3.780319606 Reorder the terms: 3.928571429 + x = -3.780319606 Solving 3.928571429 + x = -3.780319606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.928571429' to each side of the equation. 3.928571429 + -3.928571429 + x = -3.780319606 + -3.928571429 Combine like terms: 3.928571429 + -3.928571429 = 0.000000000 0.000000000 + x = -3.780319606 + -3.928571429 x = -3.780319606 + -3.928571429 Combine like terms: -3.780319606 + -3.928571429 = -7.708891035 x = -7.708891035 Simplifying x = -7.708891035Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.148251823, -7.708891035}Solution
x = {-0.148251823, -7.708891035}
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