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Simplifying 6x2 + -24x + -16 = 23 Reorder the terms: -16 + -24x + 6x2 = 23 Solving -16 + -24x + 6x2 = 23 Solving for variable 'x'. Reorder the terms: -16 + -23 + -24x + 6x2 = 23 + -23 Combine like terms: -16 + -23 = -39 -39 + -24x + 6x2 = 23 + -23 Combine like terms: 23 + -23 = 0 -39 + -24x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-13 + -8x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-13 + -8x + 2x2)' equal to zero and attempt to solve: Simplifying -13 + -8x + 2x2 = 0 Solving -13 + -8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6.5 + -4x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + -4x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + -4x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + -4x + x2 = 0 + 6.5 -4x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 -4x + x2 = 6.5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 6.5 + 4 Reorder the terms: 4 + -4x + x2 = 6.5 + 4 Combine like terms: 6.5 + 4 = 10.5 4 + -4x + x2 = 10.5 Factor a perfect square on the left side: (x + -2)(x + -2) = 10.5 Calculate the square root of the right side: 3.240370349 Break this problem into two subproblems by setting (x + -2) equal to 3.240370349 and -3.240370349.Subproblem 1
x + -2 = 3.240370349 Simplifying x + -2 = 3.240370349 Reorder the terms: -2 + x = 3.240370349 Solving -2 + x = 3.240370349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.240370349 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.240370349 + 2 x = 3.240370349 + 2 Combine like terms: 3.240370349 + 2 = 5.240370349 x = 5.240370349 Simplifying x = 5.240370349Subproblem 2
x + -2 = -3.240370349 Simplifying x + -2 = -3.240370349 Reorder the terms: -2 + x = -3.240370349 Solving -2 + x = -3.240370349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.240370349 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.240370349 + 2 x = -3.240370349 + 2 Combine like terms: -3.240370349 + 2 = -1.240370349 x = -1.240370349 Simplifying x = -1.240370349Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.240370349, -1.240370349}Solution
x = {5.240370349, -1.240370349}
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