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Simplifying 3x(2x + -5) = 6 Reorder the terms: 3x(-5 + 2x) = 6 (-5 * 3x + 2x * 3x) = 6 (-15x + 6x2) = 6 Solving -15x + 6x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + -15x + 6x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -15x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + -5x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -5x + 2x2)' equal to zero and attempt to solve: Simplifying -2 + -5x + 2x2 = 0 Solving -2 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1 + -2.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -2.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.5x + x2 = 0 + 1 -2.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2.5x + x2 = 1 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 1 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 1 + 1.5625 Combine like terms: 1 + 1.5625 = 2.5625 1.5625 + -2.5x + x2 = 2.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (x + -1.25) equal to 1.600781059 and -1.600781059.Subproblem 1
x + -1.25 = 1.600781059 Simplifying x + -1.25 = 1.600781059 Reorder the terms: -1.25 + x = 1.600781059 Solving -1.25 + x = 1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.600781059 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.600781059 + 1.25 x = 1.600781059 + 1.25 Combine like terms: 1.600781059 + 1.25 = 2.850781059 x = 2.850781059 Simplifying x = 2.850781059Subproblem 2
x + -1.25 = -1.600781059 Simplifying x + -1.25 = -1.600781059 Reorder the terms: -1.25 + x = -1.600781059 Solving -1.25 + x = -1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.600781059 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.600781059 + 1.25 x = -1.600781059 + 1.25 Combine like terms: -1.600781059 + 1.25 = -0.350781059 x = -0.350781059 Simplifying x = -0.350781059Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.850781059, -0.350781059}Solution
x = {2.850781059, -0.350781059}
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