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Simplifying 6x2 + -48x + -21 = 0 Reorder the terms: -21 + -48x + 6x2 = 0 Solving -21 + -48x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + -16x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -16x + 2x2)' equal to zero and attempt to solve: Simplifying -7 + -16x + 2x2 = 0 Solving -7 + -16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -8x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -8x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -8x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -8x + x2 = 0 + 3.5 -8x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -8x + x2 = 3.5 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 3.5 + 16 Reorder the terms: 16 + -8x + x2 = 3.5 + 16 Combine like terms: 3.5 + 16 = 19.5 16 + -8x + x2 = 19.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 19.5 Calculate the square root of the right side: 4.415880433 Break this problem into two subproblems by setting (x + -4) equal to 4.415880433 and -4.415880433.Subproblem 1
x + -4 = 4.415880433 Simplifying x + -4 = 4.415880433 Reorder the terms: -4 + x = 4.415880433 Solving -4 + x = 4.415880433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.415880433 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.415880433 + 4 x = 4.415880433 + 4 Combine like terms: 4.415880433 + 4 = 8.415880433 x = 8.415880433 Simplifying x = 8.415880433Subproblem 2
x + -4 = -4.415880433 Simplifying x + -4 = -4.415880433 Reorder the terms: -4 + x = -4.415880433 Solving -4 + x = -4.415880433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.415880433 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.415880433 + 4 x = -4.415880433 + 4 Combine like terms: -4.415880433 + 4 = -0.415880433 x = -0.415880433 Simplifying x = -0.415880433Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.415880433, -0.415880433}Solution
x = {8.415880433, -0.415880433}
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