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Simplifying 3(2x + 5) = 2(4x + -5) * 3x Reorder the terms: 3(5 + 2x) = 2(4x + -5) * 3x (5 * 3 + 2x * 3) = 2(4x + -5) * 3x (15 + 6x) = 2(4x + -5) * 3x Reorder the terms: 15 + 6x = 2(-5 + 4x) * 3x Reorder the terms for easier multiplication: 15 + 6x = 2 * 3x(-5 + 4x) Multiply 2 * 3 15 + 6x = 6x(-5 + 4x) 15 + 6x = (-5 * 6x + 4x * 6x) 15 + 6x = (-30x + 24x2) Solving 15 + 6x = -30x + 24x2 Solving for variable 'x'. Combine like terms: 6x + 30x = 36x 15 + 36x + -24x2 = -30x + 24x2 + 30x + -24x2 Reorder the terms: 15 + 36x + -24x2 = -30x + 30x + 24x2 + -24x2 Combine like terms: -30x + 30x = 0 15 + 36x + -24x2 = 0 + 24x2 + -24x2 15 + 36x + -24x2 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 15 + 36x + -24x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(5 + 12x + -8x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + 12x + -8x2)' equal to zero and attempt to solve: Simplifying 5 + 12x + -8x2 = 0 Solving 5 + 12x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.625 + -1.5x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -1.5x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -1.5x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -1.5x + x2 = 0 + 0.625 -1.5x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -1.5x + x2 = 0.625 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 0.625 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.625 + 0.5625 Combine like terms: 0.625 + 0.5625 = 1.1875 0.5625 + -1.5x + x2 = 1.1875 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 1.1875 Calculate the square root of the right side: 1.089724736 Break this problem into two subproblems by setting (x + -0.75) equal to 1.089724736 and -1.089724736.Subproblem 1
x + -0.75 = 1.089724736 Simplifying x + -0.75 = 1.089724736 Reorder the terms: -0.75 + x = 1.089724736 Solving -0.75 + x = 1.089724736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.089724736 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.089724736 + 0.75 x = 1.089724736 + 0.75 Combine like terms: 1.089724736 + 0.75 = 1.839724736 x = 1.839724736 Simplifying x = 1.839724736Subproblem 2
x + -0.75 = -1.089724736 Simplifying x + -0.75 = -1.089724736 Reorder the terms: -0.75 + x = -1.089724736 Solving -0.75 + x = -1.089724736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.089724736 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.089724736 + 0.75 x = -1.089724736 + 0.75 Combine like terms: -1.089724736 + 0.75 = -0.339724736 x = -0.339724736 Simplifying x = -0.339724736Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.839724736, -0.339724736}Solution
x = {1.839724736, -0.339724736}
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