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Simplifying 7x2 + 56x + -91 = 0 Reorder the terms: -91 + 56x + 7x2 = 0 Solving -91 + 56x + 7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(-13 + 8x + x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-13 + 8x + x2)' equal to zero and attempt to solve: Simplifying -13 + 8x + x2 = 0 Solving -13 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 8x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 8x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 8x + x2 = 0 + 13 8x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 8x + x2 = 13 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 13 + 16 Reorder the terms: 16 + 8x + x2 = 13 + 16 Combine like terms: 13 + 16 = 29 16 + 8x + x2 = 29 Factor a perfect square on the left side: (x + 4)(x + 4) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + 4) equal to 5.385164807 and -5.385164807.Subproblem 1
x + 4 = 5.385164807 Simplifying x + 4 = 5.385164807 Reorder the terms: 4 + x = 5.385164807 Solving 4 + x = 5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 5.385164807 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.385164807 + -4 x = 5.385164807 + -4 Combine like terms: 5.385164807 + -4 = 1.385164807 x = 1.385164807 Simplifying x = 1.385164807Subproblem 2
x + 4 = -5.385164807 Simplifying x + 4 = -5.385164807 Reorder the terms: 4 + x = -5.385164807 Solving 4 + x = -5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -5.385164807 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.385164807 + -4 x = -5.385164807 + -4 Combine like terms: -5.385164807 + -4 = -9.385164807 x = -9.385164807 Simplifying x = -9.385164807Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.385164807, -9.385164807}Solution
x = {1.385164807, -9.385164807}
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