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Simplifying 5x(6 + -3x) = 12 (6 * 5x + -3x * 5x) = 12 (30x + -15x2) = 12 Solving 30x + -15x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 30x + -15x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 30x + -15x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 10x + -5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + 10x + -5x2)' equal to zero and attempt to solve: Simplifying -4 + 10x + -5x2 = 0 Solving -4 + 10x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 0.8 + -2x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -2x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -2x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -2x + x2 = 0 + -0.8 -2x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -2x + x2 = -0.8 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.8 + 1 Reorder the terms: 1 + -2x + x2 = -0.8 + 1 Combine like terms: -0.8 + 1 = 0.2 1 + -2x + x2 = 0.2 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.2 Calculate the square root of the right side: 0.447213596 Break this problem into two subproblems by setting (x + -1) equal to 0.447213596 and -0.447213596.Subproblem 1
x + -1 = 0.447213596 Simplifying x + -1 = 0.447213596 Reorder the terms: -1 + x = 0.447213596 Solving -1 + x = 0.447213596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.447213596 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.447213596 + 1 x = 0.447213596 + 1 Combine like terms: 0.447213596 + 1 = 1.447213596 x = 1.447213596 Simplifying x = 1.447213596Subproblem 2
x + -1 = -0.447213596 Simplifying x + -1 = -0.447213596 Reorder the terms: -1 + x = -0.447213596 Solving -1 + x = -0.447213596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.447213596 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.447213596 + 1 x = -0.447213596 + 1 Combine like terms: -0.447213596 + 1 = 0.552786404 x = 0.552786404 Simplifying x = 0.552786404Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.447213596, 0.552786404}Solution
x = {1.447213596, 0.552786404}
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