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Simplifying 6x2 + -24x = 64 Reorder the terms: -24x + 6x2 = 64 Solving -24x + 6x2 = 64 Solving for variable 'x'. Reorder the terms: -64 + -24x + 6x2 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + -24x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-32 + -12x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-32 + -12x + 3x2)' equal to zero and attempt to solve: Simplifying -32 + -12x + 3x2 = 0 Solving -32 + -12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10.66666667 + -4x + x2 = 0 Move the constant term to the right: Add '10.66666667' to each side of the equation. -10.66666667 + -4x + 10.66666667 + x2 = 0 + 10.66666667 Reorder the terms: -10.66666667 + 10.66666667 + -4x + x2 = 0 + 10.66666667 Combine like terms: -10.66666667 + 10.66666667 = 0.00000000 0.00000000 + -4x + x2 = 0 + 10.66666667 -4x + x2 = 0 + 10.66666667 Combine like terms: 0 + 10.66666667 = 10.66666667 -4x + x2 = 10.66666667 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 = 10.66666667 + 4 Reorder the terms: 4 + -4x + x2 = 10.66666667 + 4 Combine like terms: 10.66666667 + 4 = 14.66666667 4 + -4x + x2 = 14.66666667 Factor a perfect square on the left side: (x + -2)(x + -2) = 14.66666667 Calculate the square root of the right side: 3.829708431 Break this problem into two subproblems by setting (x + -2) equal to 3.829708431 and -3.829708431.Subproblem 1
x + -2 = 3.829708431 Simplifying x + -2 = 3.829708431 Reorder the terms: -2 + x = 3.829708431 Solving -2 + x = 3.829708431 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 = 3.829708431 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.829708431 + 2 x = 3.829708431 + 2 Combine like terms: 3.829708431 + 2 = 5.829708431 x = 5.829708431 Simplifying x = 5.829708431Subproblem 2
x + -2 = -3.829708431 Simplifying x + -2 = -3.829708431 Reorder the terms: -2 + x = -3.829708431 Solving -2 + x = -3.829708431 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 = -3.829708431 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.829708431 + 2 x = -3.829708431 + 2 Combine like terms: -3.829708431 + 2 = -1.829708431 x = -1.829708431 Simplifying x = -1.829708431Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.829708431, -1.829708431}Solution
x = {5.829708431, -1.829708431}
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