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Simplifying -5(x + 1) * 3x + 2 = 6x + 4 Reorder the terms: -5(1 + x) * 3x + 2 = 6x + 4 Reorder the terms for easier multiplication: -5 * 3x(1 + x) + 2 = 6x + 4 Multiply -5 * 3 -15x(1 + x) + 2 = 6x + 4 (1 * -15x + x * -15x) + 2 = 6x + 4 (-15x + -15x2) + 2 = 6x + 4 Reorder the terms: 2 + -15x + -15x2 = 6x + 4 Reorder the terms: 2 + -15x + -15x2 = 4 + 6x Solving 2 + -15x + -15x2 = 4 + 6x Solving for variable 'x'. Reorder the terms: 2 + -4 + -15x + -6x + -15x2 = 4 + 6x + -4 + -6x Combine like terms: 2 + -4 = -2 -2 + -15x + -6x + -15x2 = 4 + 6x + -4 + -6x Combine like terms: -15x + -6x = -21x -2 + -21x + -15x2 = 4 + 6x + -4 + -6x Reorder the terms: -2 + -21x + -15x2 = 4 + -4 + 6x + -6x Combine like terms: 4 + -4 = 0 -2 + -21x + -15x2 = 0 + 6x + -6x -2 + -21x + -15x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -2 + -21x + -15x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 21x + 15x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 21x + 15x2)' equal to zero and attempt to solve: Simplifying 2 + 21x + 15x2 = 0 Solving 2 + 21x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.1333333333 + 1.4x + x2 = 0 Move the constant term to the right: Add '-0.1333333333' to each side of the equation. 0.1333333333 + 1.4x + -0.1333333333 + x2 = 0 + -0.1333333333 Reorder the terms: 0.1333333333 + -0.1333333333 + 1.4x + x2 = 0 + -0.1333333333 Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000 0.0000000000 + 1.4x + x2 = 0 + -0.1333333333 1.4x + x2 = 0 + -0.1333333333 Combine like terms: 0 + -0.1333333333 = -0.1333333333 1.4x + x2 = -0.1333333333 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = -0.1333333333 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = -0.1333333333 + 0.49 Combine like terms: -0.1333333333 + 0.49 = 0.3566666667 0.49 + 1.4x + x2 = 0.3566666667 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 0.3566666667 Calculate the square root of the right side: 0.597215762 Break this problem into two subproblems by setting (x + 0.7) equal to 0.597215762 and -0.597215762.Subproblem 1
x + 0.7 = 0.597215762 Simplifying x + 0.7 = 0.597215762 Reorder the terms: 0.7 + x = 0.597215762 Solving 0.7 + x = 0.597215762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 0.597215762 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 0.597215762 + -0.7 x = 0.597215762 + -0.7 Combine like terms: 0.597215762 + -0.7 = -0.102784238 x = -0.102784238 Simplifying x = -0.102784238Subproblem 2
x + 0.7 = -0.597215762 Simplifying x + 0.7 = -0.597215762 Reorder the terms: 0.7 + x = -0.597215762 Solving 0.7 + x = -0.597215762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -0.597215762 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -0.597215762 + -0.7 x = -0.597215762 + -0.7 Combine like terms: -0.597215762 + -0.7 = -1.297215762 x = -1.297215762 Simplifying x = -1.297215762Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.102784238, -1.297215762}Solution
x = {-0.102784238, -1.297215762}
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