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Simplifying x + 5(x + -4) = 3x(x + -8) + -5 Reorder the terms: x + 5(-4 + x) = 3x(x + -8) + -5 x + (-4 * 5 + x * 5) = 3x(x + -8) + -5 x + (-20 + 5x) = 3x(x + -8) + -5 Reorder the terms: -20 + x + 5x = 3x(x + -8) + -5 Combine like terms: x + 5x = 6x -20 + 6x = 3x(x + -8) + -5 Reorder the terms: -20 + 6x = 3x(-8 + x) + -5 -20 + 6x = (-8 * 3x + x * 3x) + -5 -20 + 6x = (-24x + 3x2) + -5 Reorder the terms: -20 + 6x = -5 + -24x + 3x2 Solving -20 + 6x = -5 + -24x + 3x2 Solving for variable 'x'. Reorder the terms: -20 + 5 + 6x + 24x + -3x2 = -5 + -24x + 3x2 + 5 + 24x + -3x2 Combine like terms: -20 + 5 = -15 -15 + 6x + 24x + -3x2 = -5 + -24x + 3x2 + 5 + 24x + -3x2 Combine like terms: 6x + 24x = 30x -15 + 30x + -3x2 = -5 + -24x + 3x2 + 5 + 24x + -3x2 Reorder the terms: -15 + 30x + -3x2 = -5 + 5 + -24x + 24x + 3x2 + -3x2 Combine like terms: -5 + 5 = 0 -15 + 30x + -3x2 = 0 + -24x + 24x + 3x2 + -3x2 -15 + 30x + -3x2 = -24x + 24x + 3x2 + -3x2 Combine like terms: -24x + 24x = 0 -15 + 30x + -3x2 = 0 + 3x2 + -3x2 -15 + 30x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -15 + 30x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 10x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + 10x + -1x2)' equal to zero and attempt to solve: Simplifying -5 + 10x + -1x2 = 0 Solving -5 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5 + -10x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -10x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -10x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -10x + x2 = 0 + -5 -10x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -10x + x2 = -5 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -5 + 25 Reorder the terms: 25 + -10x + x2 = -5 + 25 Combine like terms: -5 + 25 = 20 25 + -10x + x2 = 20 Factor a perfect square on the left side: (x + -5)(x + -5) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + -5) equal to 4.472135955 and -4.472135955.Subproblem 1
x + -5 = 4.472135955 Simplifying x + -5 = 4.472135955 Reorder the terms: -5 + x = 4.472135955 Solving -5 + x = 4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.472135955 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.472135955 + 5 x = 4.472135955 + 5 Combine like terms: 4.472135955 + 5 = 9.472135955 x = 9.472135955 Simplifying x = 9.472135955Subproblem 2
x + -5 = -4.472135955 Simplifying x + -5 = -4.472135955 Reorder the terms: -5 + x = -4.472135955 Solving -5 + x = -4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.472135955 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.472135955 + 5 x = -4.472135955 + 5 Combine like terms: -4.472135955 + 5 = 0.527864045 x = 0.527864045 Simplifying x = 0.527864045Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.472135955, 0.527864045}Solution
x = {9.472135955, 0.527864045}
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