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Simplifying -5x2 + -34x + -8 = 0 Reorder the terms: -8 + -34x + -5x2 = 0 Solving -8 + -34x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 34x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 34x + 5x2)' equal to zero and attempt to solve: Simplifying 8 + 34x + 5x2 = 0 Solving 8 + 34x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.6 + 6.8x + x2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + 6.8x + -1.6 + x2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + 6.8x + x2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + 6.8x + x2 = 0 + -1.6 6.8x + x2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 6.8x + x2 = -1.6 The x term is 6.8x. Take half its coefficient (3.4). Square it (11.56) and add it to both sides. Add '11.56' to each side of the equation. 6.8x + 11.56 + x2 = -1.6 + 11.56 Reorder the terms: 11.56 + 6.8x + x2 = -1.6 + 11.56 Combine like terms: -1.6 + 11.56 = 9.96 11.56 + 6.8x + x2 = 9.96 Factor a perfect square on the left side: (x + 3.4)(x + 3.4) = 9.96 Calculate the square root of the right side: 3.155946768 Break this problem into two subproblems by setting (x + 3.4) equal to 3.155946768 and -3.155946768.Subproblem 1
x + 3.4 = 3.155946768 Simplifying x + 3.4 = 3.155946768 Reorder the terms: 3.4 + x = 3.155946768 Solving 3.4 + x = 3.155946768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.4' to each side of the equation. 3.4 + -3.4 + x = 3.155946768 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + x = 3.155946768 + -3.4 x = 3.155946768 + -3.4 Combine like terms: 3.155946768 + -3.4 = -0.244053232 x = -0.244053232 Simplifying x = -0.244053232Subproblem 2
x + 3.4 = -3.155946768 Simplifying x + 3.4 = -3.155946768 Reorder the terms: 3.4 + x = -3.155946768 Solving 3.4 + x = -3.155946768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.4' to each side of the equation. 3.4 + -3.4 + x = -3.155946768 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + x = -3.155946768 + -3.4 x = -3.155946768 + -3.4 Combine like terms: -3.155946768 + -3.4 = -6.555946768 x = -6.555946768 Simplifying x = -6.555946768Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.244053232, -6.555946768}Solution
x = {-0.244053232, -6.555946768}
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