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Simplifying 34x2 + 88x + 32 = 0 Reorder the terms: 32 + 88x + 34x2 = 0 Solving 32 + 88x + 34x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(16 + 44x + 17x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(16 + 44x + 17x2)' equal to zero and attempt to solve: Simplifying 16 + 44x + 17x2 = 0 Solving 16 + 44x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 0.9411764706 + 2.588235294x + x2 = 0 Move the constant term to the right: Add '-0.9411764706' to each side of the equation. 0.9411764706 + 2.588235294x + -0.9411764706 + x2 = 0 + -0.9411764706 Reorder the terms: 0.9411764706 + -0.9411764706 + 2.588235294x + x2 = 0 + -0.9411764706 Combine like terms: 0.9411764706 + -0.9411764706 = 0.0000000000 0.0000000000 + 2.588235294x + x2 = 0 + -0.9411764706 2.588235294x + x2 = 0 + -0.9411764706 Combine like terms: 0 + -0.9411764706 = -0.9411764706 2.588235294x + x2 = -0.9411764706 The x term is 2.588235294x. Take half its coefficient (1.294117647). Square it (1.674740484) and add it to both sides. Add '1.674740484' to each side of the equation. 2.588235294x + 1.674740484 + x2 = -0.9411764706 + 1.674740484 Reorder the terms: 1.674740484 + 2.588235294x + x2 = -0.9411764706 + 1.674740484 Combine like terms: -0.9411764706 + 1.674740484 = 0.7335640134 1.674740484 + 2.588235294x + x2 = 0.7335640134 Factor a perfect square on the left side: (x + 1.294117647)(x + 1.294117647) = 0.7335640134 Calculate the square root of the right side: 0.856483516 Break this problem into two subproblems by setting (x + 1.294117647) equal to 0.856483516 and -0.856483516.Subproblem 1
x + 1.294117647 = 0.856483516 Simplifying x + 1.294117647 = 0.856483516 Reorder the terms: 1.294117647 + x = 0.856483516 Solving 1.294117647 + x = 0.856483516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.294117647' to each side of the equation. 1.294117647 + -1.294117647 + x = 0.856483516 + -1.294117647 Combine like terms: 1.294117647 + -1.294117647 = 0.000000000 0.000000000 + x = 0.856483516 + -1.294117647 x = 0.856483516 + -1.294117647 Combine like terms: 0.856483516 + -1.294117647 = -0.437634131 x = -0.437634131 Simplifying x = -0.437634131Subproblem 2
x + 1.294117647 = -0.856483516 Simplifying x + 1.294117647 = -0.856483516 Reorder the terms: 1.294117647 + x = -0.856483516 Solving 1.294117647 + x = -0.856483516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.294117647' to each side of the equation. 1.294117647 + -1.294117647 + x = -0.856483516 + -1.294117647 Combine like terms: 1.294117647 + -1.294117647 = 0.000000000 0.000000000 + x = -0.856483516 + -1.294117647 x = -0.856483516 + -1.294117647 Combine like terms: -0.856483516 + -1.294117647 = -2.150601163 x = -2.150601163 Simplifying x = -2.150601163Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.437634131, -2.150601163}Solution
x = {-0.437634131, -2.150601163}
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