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Simplifying 6x2 = 10x + 48 Reorder the terms: 6x2 = 48 + 10x Solving 6x2 = 48 + 10x Solving for variable 'x'. Reorder the terms: -48 + -10x + 6x2 = 48 + 10x + -48 + -10x Reorder the terms: -48 + -10x + 6x2 = 48 + -48 + 10x + -10x Combine like terms: 48 + -48 = 0 -48 + -10x + 6x2 = 0 + 10x + -10x -48 + -10x + 6x2 = 10x + -10x Combine like terms: 10x + -10x = 0 -48 + -10x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-24 + -5x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-24 + -5x + 3x2)' equal to zero and attempt to solve: Simplifying -24 + -5x + 3x2 = 0 Solving -24 + -5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -1.666666667x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -1.666666667x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1.666666667x + x2 = 0 + 8 -1.666666667x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -1.666666667x + x2 = 8 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 8 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 8 + 0.6944444447 Combine like terms: 8 + 0.6944444447 = 8.6944444447 0.6944444447 + -1.666666667x + x2 = 8.6944444447 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 8.6944444447 Calculate the square root of the right side: 2.948634336 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 2.948634336 and -2.948634336.Subproblem 1
x + -0.8333333335 = 2.948634336 Simplifying x + -0.8333333335 = 2.948634336 Reorder the terms: -0.8333333335 + x = 2.948634336 Solving -0.8333333335 + x = 2.948634336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 2.948634336 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 2.948634336 + 0.8333333335 x = 2.948634336 + 0.8333333335 Combine like terms: 2.948634336 + 0.8333333335 = 3.7819676695 x = 3.7819676695 Simplifying x = 3.7819676695Subproblem 2
x + -0.8333333335 = -2.948634336 Simplifying x + -0.8333333335 = -2.948634336 Reorder the terms: -0.8333333335 + x = -2.948634336 Solving -0.8333333335 + x = -2.948634336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -2.948634336 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -2.948634336 + 0.8333333335 x = -2.948634336 + 0.8333333335 Combine like terms: -2.948634336 + 0.8333333335 = -2.1153010025 x = -2.1153010025 Simplifying x = -2.1153010025Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.7819676695, -2.1153010025}Solution
x = {3.7819676695, -2.1153010025}
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