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Simplifying 3x(5x + -2) = 24 Reorder the terms: 3x(-2 + 5x) = 24 (-2 * 3x + 5x * 3x) = 24 (-6x + 15x2) = 24 Solving -6x + 15x2 = 24 Solving for variable 'x'. Reorder the terms: -24 + -6x + 15x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + -6x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-8 + -2x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-8 + -2x + 5x2)' equal to zero and attempt to solve: Simplifying -8 + -2x + 5x2 = 0 Solving -8 + -2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + -0.4x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -0.4x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -0.4x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -0.4x + x2 = 0 + 1.6 -0.4x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -0.4x + x2 = 1.6 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 1.6 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 1.6 + 0.04 Combine like terms: 1.6 + 0.04 = 1.64 0.04 + -0.4x + x2 = 1.64 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 1.64 Calculate the square root of the right side: 1.280624847 Break this problem into two subproblems by setting (x + -0.2) equal to 1.280624847 and -1.280624847.Subproblem 1
x + -0.2 = 1.280624847 Simplifying x + -0.2 = 1.280624847 Reorder the terms: -0.2 + x = 1.280624847 Solving -0.2 + x = 1.280624847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 1.280624847 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 1.280624847 + 0.2 x = 1.280624847 + 0.2 Combine like terms: 1.280624847 + 0.2 = 1.480624847 x = 1.480624847 Simplifying x = 1.480624847Subproblem 2
x + -0.2 = -1.280624847 Simplifying x + -0.2 = -1.280624847 Reorder the terms: -0.2 + x = -1.280624847 Solving -0.2 + x = -1.280624847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -1.280624847 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -1.280624847 + 0.2 x = -1.280624847 + 0.2 Combine like terms: -1.280624847 + 0.2 = -1.080624847 x = -1.080624847 Simplifying x = -1.080624847Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.480624847, -1.080624847}Solution
x = {1.480624847, -1.080624847}
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