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Simplifying 3x(5x + 2) = 5x(x + 6) + 26 Reorder the terms: 3x(2 + 5x) = 5x(x + 6) + 26 (2 * 3x + 5x * 3x) = 5x(x + 6) + 26 (6x + 15x2) = 5x(x + 6) + 26 Reorder the terms: 6x + 15x2 = 5x(6 + x) + 26 6x + 15x2 = (6 * 5x + x * 5x) + 26 6x + 15x2 = (30x + 5x2) + 26 Reorder the terms: 6x + 15x2 = 26 + 30x + 5x2 Solving 6x + 15x2 = 26 + 30x + 5x2 Solving for variable 'x'. Reorder the terms: -26 + 6x + -30x + 15x2 + -5x2 = 26 + 30x + 5x2 + -26 + -30x + -5x2 Combine like terms: 6x + -30x = -24x -26 + -24x + 15x2 + -5x2 = 26 + 30x + 5x2 + -26 + -30x + -5x2 Combine like terms: 15x2 + -5x2 = 10x2 -26 + -24x + 10x2 = 26 + 30x + 5x2 + -26 + -30x + -5x2 Reorder the terms: -26 + -24x + 10x2 = 26 + -26 + 30x + -30x + 5x2 + -5x2 Combine like terms: 26 + -26 = 0 -26 + -24x + 10x2 = 0 + 30x + -30x + 5x2 + -5x2 -26 + -24x + 10x2 = 30x + -30x + 5x2 + -5x2 Combine like terms: 30x + -30x = 0 -26 + -24x + 10x2 = 0 + 5x2 + -5x2 -26 + -24x + 10x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -26 + -24x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + -12x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + -12x + 5x2)' equal to zero and attempt to solve: Simplifying -13 + -12x + 5x2 = 0 Solving -13 + -12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.6 + -2.4x + x2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + -2.4x + 2.6 + x2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + -2.4x + x2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + -2.4x + x2 = 0 + 2.6 -2.4x + x2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 -2.4x + x2 = 2.6 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = 2.6 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 2.6 + 1.44 Combine like terms: 2.6 + 1.44 = 4.04 1.44 + -2.4x + x2 = 4.04 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 4.04 Calculate the square root of the right side: 2.009975124 Break this problem into two subproblems by setting (x + -1.2) equal to 2.009975124 and -2.009975124.Subproblem 1
x + -1.2 = 2.009975124 Simplifying x + -1.2 = 2.009975124 Reorder the terms: -1.2 + x = 2.009975124 Solving -1.2 + x = 2.009975124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 2.009975124 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 2.009975124 + 1.2 x = 2.009975124 + 1.2 Combine like terms: 2.009975124 + 1.2 = 3.209975124 x = 3.209975124 Simplifying x = 3.209975124Subproblem 2
x + -1.2 = -2.009975124 Simplifying x + -1.2 = -2.009975124 Reorder the terms: -1.2 + x = -2.009975124 Solving -1.2 + x = -2.009975124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -2.009975124 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -2.009975124 + 1.2 x = -2.009975124 + 1.2 Combine like terms: -2.009975124 + 1.2 = -0.809975124 x = -0.809975124 Simplifying x = -0.809975124Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.209975124, -0.809975124}Solution
x = {3.209975124, -0.809975124}
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