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Simplifying 34x2 + -4x + 8 = 100 Reorder the terms: 8 + -4x + 34x2 = 100 Solving 8 + -4x + 34x2 = 100 Solving for variable 'x'. Reorder the terms: 8 + -100 + -4x + 34x2 = 100 + -100 Combine like terms: 8 + -100 = -92 -92 + -4x + 34x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -92 + -4x + 34x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-46 + -2x + 17x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-46 + -2x + 17x2)' equal to zero and attempt to solve: Simplifying -46 + -2x + 17x2 = 0 Solving -46 + -2x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -2.705882353 + -0.1176470588x + x2 = 0 Move the constant term to the right: Add '2.705882353' to each side of the equation. -2.705882353 + -0.1176470588x + 2.705882353 + x2 = 0 + 2.705882353 Reorder the terms: -2.705882353 + 2.705882353 + -0.1176470588x + x2 = 0 + 2.705882353 Combine like terms: -2.705882353 + 2.705882353 = 0.000000000 0.000000000 + -0.1176470588x + x2 = 0 + 2.705882353 -0.1176470588x + x2 = 0 + 2.705882353 Combine like terms: 0 + 2.705882353 = 2.705882353 -0.1176470588x + x2 = 2.705882353 The x term is -0.1176470588x. Take half its coefficient (-0.0588235294). Square it (0.003460207611) and add it to both sides. Add '0.003460207611' to each side of the equation. -0.1176470588x + 0.003460207611 + x2 = 2.705882353 + 0.003460207611 Reorder the terms: 0.003460207611 + -0.1176470588x + x2 = 2.705882353 + 0.003460207611 Combine like terms: 2.705882353 + 0.003460207611 = 2.709342560611 0.003460207611 + -0.1176470588x + x2 = 2.709342560611 Factor a perfect square on the left side: (x + -0.0588235294)(x + -0.0588235294) = 2.709342560611 Calculate the square root of the right side: 1.646008068 Break this problem into two subproblems by setting (x + -0.0588235294) equal to 1.646008068 and -1.646008068.Subproblem 1
x + -0.0588235294 = 1.646008068 Simplifying x + -0.0588235294 = 1.646008068 Reorder the terms: -0.0588235294 + x = 1.646008068 Solving -0.0588235294 + x = 1.646008068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0588235294' to each side of the equation. -0.0588235294 + 0.0588235294 + x = 1.646008068 + 0.0588235294 Combine like terms: -0.0588235294 + 0.0588235294 = 0.0000000000 0.0000000000 + x = 1.646008068 + 0.0588235294 x = 1.646008068 + 0.0588235294 Combine like terms: 1.646008068 + 0.0588235294 = 1.7048315974 x = 1.7048315974 Simplifying x = 1.7048315974Subproblem 2
x + -0.0588235294 = -1.646008068 Simplifying x + -0.0588235294 = -1.646008068 Reorder the terms: -0.0588235294 + x = -1.646008068 Solving -0.0588235294 + x = -1.646008068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0588235294' to each side of the equation. -0.0588235294 + 0.0588235294 + x = -1.646008068 + 0.0588235294 Combine like terms: -0.0588235294 + 0.0588235294 = 0.0000000000 0.0000000000 + x = -1.646008068 + 0.0588235294 x = -1.646008068 + 0.0588235294 Combine like terms: -1.646008068 + 0.0588235294 = -1.5871845386 x = -1.5871845386 Simplifying x = -1.5871845386Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7048315974, -1.5871845386}Solution
x = {1.7048315974, -1.5871845386}
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