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Simplifying (4x + 3)(6x + -1) = 9 + -34x Reorder the terms: (3 + 4x)(6x + -1) = 9 + -34x Reorder the terms: (3 + 4x)(-1 + 6x) = 9 + -34x Multiply (3 + 4x) * (-1 + 6x) (3(-1 + 6x) + 4x * (-1 + 6x)) = 9 + -34x ((-1 * 3 + 6x * 3) + 4x * (-1 + 6x)) = 9 + -34x ((-3 + 18x) + 4x * (-1 + 6x)) = 9 + -34x (-3 + 18x + (-1 * 4x + 6x * 4x)) = 9 + -34x (-3 + 18x + (-4x + 24x2)) = 9 + -34x Combine like terms: 18x + -4x = 14x (-3 + 14x + 24x2) = 9 + -34x Solving -3 + 14x + 24x2 = 9 + -34x Solving for variable 'x'. Reorder the terms: -3 + -9 + 14x + 34x + 24x2 = 9 + -34x + -9 + 34x Combine like terms: -3 + -9 = -12 -12 + 14x + 34x + 24x2 = 9 + -34x + -9 + 34x Combine like terms: 14x + 34x = 48x -12 + 48x + 24x2 = 9 + -34x + -9 + 34x Reorder the terms: -12 + 48x + 24x2 = 9 + -9 + -34x + 34x Combine like terms: 9 + -9 = 0 -12 + 48x + 24x2 = 0 + -34x + 34x -12 + 48x + 24x2 = -34x + 34x Combine like terms: -34x + 34x = 0 -12 + 48x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(-1 + 4x + 2x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-1 + 4x + 2x2)' equal to zero and attempt to solve: Simplifying -1 + 4x + 2x2 = 0 Solving -1 + 4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + 2x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 2x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 2x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 2x + x2 = 0 + 0.5 2x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 2x + x2 = 0.5 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 = 0.5 + 1 Reorder the terms: 1 + 2x + x2 = 0.5 + 1 Combine like terms: 0.5 + 1 = 1.5 1 + 2x + x2 = 1.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + 1) equal to 1.224744871 and -1.224744871.Subproblem 1
x + 1 = 1.224744871 Simplifying x + 1 = 1.224744871 Reorder the terms: 1 + x = 1.224744871 Solving 1 + x = 1.224744871 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 = 1.224744871 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.224744871 + -1 x = 1.224744871 + -1 Combine like terms: 1.224744871 + -1 = 0.224744871 x = 0.224744871 Simplifying x = 0.224744871Subproblem 2
x + 1 = -1.224744871 Simplifying x + 1 = -1.224744871 Reorder the terms: 1 + x = -1.224744871 Solving 1 + x = -1.224744871 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 = -1.224744871 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.224744871 + -1 x = -1.224744871 + -1 Combine like terms: -1.224744871 + -1 = -2.224744871 x = -2.224744871 Simplifying x = -2.224744871Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.224744871, -2.224744871}Solution
x = {0.224744871, -2.224744871}
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