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Simplifying x + 3(8x + 4) = 5x(4 + 2x) Reorder the terms: x + 3(4 + 8x) = 5x(4 + 2x) x + (4 * 3 + 8x * 3) = 5x(4 + 2x) x + (12 + 24x) = 5x(4 + 2x) Reorder the terms: 12 + x + 24x = 5x(4 + 2x) Combine like terms: x + 24x = 25x 12 + 25x = 5x(4 + 2x) 12 + 25x = (4 * 5x + 2x * 5x) 12 + 25x = (20x + 10x2) Solving 12 + 25x = 20x + 10x2 Solving for variable 'x'. Combine like terms: 25x + -20x = 5x 12 + 5x + -10x2 = 20x + 10x2 + -20x + -10x2 Reorder the terms: 12 + 5x + -10x2 = 20x + -20x + 10x2 + -10x2 Combine like terms: 20x + -20x = 0 12 + 5x + -10x2 = 0 + 10x2 + -10x2 12 + 5x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 12 + 5x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -1.2 + -0.5x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -0.5x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -0.5x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -0.5x + x2 = 0 + 1.2 -0.5x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -0.5x + x2 = 1.2 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 1.2 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 1.2 + 0.0625 Combine like terms: 1.2 + 0.0625 = 1.2625 0.0625 + -0.5x + x2 = 1.2625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 1.2625 Calculate the square root of the right side: 1.123610253 Break this problem into two subproblems by setting (x + -0.25) equal to 1.123610253 and -1.123610253.Subproblem 1
x + -0.25 = 1.123610253 Simplifying x + -0.25 = 1.123610253 Reorder the terms: -0.25 + x = 1.123610253 Solving -0.25 + x = 1.123610253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.123610253 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.123610253 + 0.25 x = 1.123610253 + 0.25 Combine like terms: 1.123610253 + 0.25 = 1.373610253 x = 1.373610253 Simplifying x = 1.373610253Subproblem 2
x + -0.25 = -1.123610253 Simplifying x + -0.25 = -1.123610253 Reorder the terms: -0.25 + x = -1.123610253 Solving -0.25 + x = -1.123610253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.123610253 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.123610253 + 0.25 x = -1.123610253 + 0.25 Combine like terms: -1.123610253 + 0.25 = -0.873610253 x = -0.873610253 Simplifying x = -0.873610253Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.373610253, -0.873610253}
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