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Simplifying 5 + -6x(7 + x) + 5 = 8 5 + (7 * -6x + x * -6x) + 5 = 8 5 + (-42x + -6x2) + 5 = 8 Reorder the terms: 5 + 5 + -42x + -6x2 = 8 Combine like terms: 5 + 5 = 10 10 + -42x + -6x2 = 8 Solving 10 + -42x + -6x2 = 8 Solving for variable 'x'. Reorder the terms: 10 + -8 + -42x + -6x2 = 8 + -8 Combine like terms: 10 + -8 = 2 2 + -42x + -6x2 = 8 + -8 Combine like terms: 8 + -8 = 0 2 + -42x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -21x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -21x + -3x2)' equal to zero and attempt to solve: Simplifying 1 + -21x + -3x2 = 0 Solving 1 + -21x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -0.3333333333 + 7x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 7x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 7x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 7x + x2 = 0 + 0.3333333333 7x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 7x + x2 = 0.3333333333 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 0.3333333333 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 0.3333333333 + 12.25 Combine like terms: 0.3333333333 + 12.25 = 12.5833333333 12.25 + 7x + x2 = 12.5833333333 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 12.5833333333 Calculate the square root of the right side: 3.547299442 Break this problem into two subproblems by setting (x + 3.5) equal to 3.547299442 and -3.547299442.Subproblem 1
x + 3.5 = 3.547299442 Simplifying x + 3.5 = 3.547299442 Reorder the terms: 3.5 + x = 3.547299442 Solving 3.5 + x = 3.547299442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.547299442 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.547299442 + -3.5 x = 3.547299442 + -3.5 Combine like terms: 3.547299442 + -3.5 = 0.047299442 x = 0.047299442 Simplifying x = 0.047299442Subproblem 2
x + 3.5 = -3.547299442 Simplifying x + 3.5 = -3.547299442 Reorder the terms: 3.5 + x = -3.547299442 Solving 3.5 + x = -3.547299442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.547299442 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.547299442 + -3.5 x = -3.547299442 + -3.5 Combine like terms: -3.547299442 + -3.5 = -7.047299442 x = -7.047299442 Simplifying x = -7.047299442Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.047299442, -7.047299442}Solution
x = {0.047299442, -7.047299442}
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