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Simplifying 48x2 + 354x + -30 = 0 Reorder the terms: -30 + 354x + 48x2 = 0 Solving -30 + 354x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-5 + 59x + 8x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-5 + 59x + 8x2)' equal to zero and attempt to solve: Simplifying -5 + 59x + 8x2 = 0 Solving -5 + 59x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + 7.375x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 7.375x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 7.375x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 7.375x + x2 = 0 + 0.625 7.375x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 7.375x + x2 = 0.625 The x term is 7.375x. Take half its coefficient (3.6875). Square it (13.59765625) and add it to both sides. Add '13.59765625' to each side of the equation. 7.375x + 13.59765625 + x2 = 0.625 + 13.59765625 Reorder the terms: 13.59765625 + 7.375x + x2 = 0.625 + 13.59765625 Combine like terms: 0.625 + 13.59765625 = 14.22265625 13.59765625 + 7.375x + x2 = 14.22265625 Factor a perfect square on the left side: (x + 3.6875)(x + 3.6875) = 14.22265625 Calculate the square root of the right side: 3.77129371 Break this problem into two subproblems by setting (x + 3.6875) equal to 3.77129371 and -3.77129371.Subproblem 1
x + 3.6875 = 3.77129371 Simplifying x + 3.6875 = 3.77129371 Reorder the terms: 3.6875 + x = 3.77129371 Solving 3.6875 + x = 3.77129371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6875' to each side of the equation. 3.6875 + -3.6875 + x = 3.77129371 + -3.6875 Combine like terms: 3.6875 + -3.6875 = 0.0000 0.0000 + x = 3.77129371 + -3.6875 x = 3.77129371 + -3.6875 Combine like terms: 3.77129371 + -3.6875 = 0.08379371 x = 0.08379371 Simplifying x = 0.08379371Subproblem 2
x + 3.6875 = -3.77129371 Simplifying x + 3.6875 = -3.77129371 Reorder the terms: 3.6875 + x = -3.77129371 Solving 3.6875 + x = -3.77129371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6875' to each side of the equation. 3.6875 + -3.6875 + x = -3.77129371 + -3.6875 Combine like terms: 3.6875 + -3.6875 = 0.0000 0.0000 + x = -3.77129371 + -3.6875 x = -3.77129371 + -3.6875 Combine like terms: -3.77129371 + -3.6875 = -7.45879371 x = -7.45879371 Simplifying x = -7.45879371Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.08379371, -7.45879371}Solution
x = {0.08379371, -7.45879371}
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