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Simplifying 56x2 + 160x + -16 = 4 Reorder the terms: -16 + 160x + 56x2 = 4 Solving -16 + 160x + 56x2 = 4 Solving for variable 'x'. Reorder the terms: -16 + -4 + 160x + 56x2 = 4 + -4 Combine like terms: -16 + -4 = -20 -20 + 160x + 56x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -20 + 160x + 56x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + 40x + 14x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + 40x + 14x2)' equal to zero and attempt to solve: Simplifying -5 + 40x + 14x2 = 0 Solving -5 + 40x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.3571428571 + 2.857142857x + x2 = 0 Move the constant term to the right: Add '0.3571428571' to each side of the equation. -0.3571428571 + 2.857142857x + 0.3571428571 + x2 = 0 + 0.3571428571 Reorder the terms: -0.3571428571 + 0.3571428571 + 2.857142857x + x2 = 0 + 0.3571428571 Combine like terms: -0.3571428571 + 0.3571428571 = 0.0000000000 0.0000000000 + 2.857142857x + x2 = 0 + 0.3571428571 2.857142857x + x2 = 0 + 0.3571428571 Combine like terms: 0 + 0.3571428571 = 0.3571428571 2.857142857x + x2 = 0.3571428571 The x term is 2.857142857x. Take half its coefficient (1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. 2.857142857x + 2.040816328 + x2 = 0.3571428571 + 2.040816328 Reorder the terms: 2.040816328 + 2.857142857x + x2 = 0.3571428571 + 2.040816328 Combine like terms: 0.3571428571 + 2.040816328 = 2.3979591851 2.040816328 + 2.857142857x + x2 = 2.3979591851 Factor a perfect square on the left side: (x + 1.428571429)(x + 1.428571429) = 2.3979591851 Calculate the square root of the right side: 1.548534528 Break this problem into two subproblems by setting (x + 1.428571429) equal to 1.548534528 and -1.548534528.Subproblem 1
x + 1.428571429 = 1.548534528 Simplifying x + 1.428571429 = 1.548534528 Reorder the terms: 1.428571429 + x = 1.548534528 Solving 1.428571429 + x = 1.548534528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + x = 1.548534528 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + x = 1.548534528 + -1.428571429 x = 1.548534528 + -1.428571429 Combine like terms: 1.548534528 + -1.428571429 = 0.119963099 x = 0.119963099 Simplifying x = 0.119963099Subproblem 2
x + 1.428571429 = -1.548534528 Simplifying x + 1.428571429 = -1.548534528 Reorder the terms: 1.428571429 + x = -1.548534528 Solving 1.428571429 + x = -1.548534528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + x = -1.548534528 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + x = -1.548534528 + -1.428571429 x = -1.548534528 + -1.428571429 Combine like terms: -1.548534528 + -1.428571429 = -2.977105957 x = -2.977105957 Simplifying x = -2.977105957Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.119963099, -2.977105957}Solution
x = {0.119963099, -2.977105957}
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