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Simplifying 4(x2 + 60x + -1728) = 0 Reorder the terms: 4(-1728 + 60x + x2) = 0 (-1728 * 4 + 60x * 4 + x2 * 4) = 0 (-6912 + 240x + 4x2) = 0 Solving -6912 + 240x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-1728 + 60x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1728 + 60x + x2)' equal to zero and attempt to solve: Simplifying -1728 + 60x + x2 = 0 Solving -1728 + 60x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1728' to each side of the equation. -1728 + 60x + 1728 + x2 = 0 + 1728 Reorder the terms: -1728 + 1728 + 60x + x2 = 0 + 1728 Combine like terms: -1728 + 1728 = 0 0 + 60x + x2 = 0 + 1728 60x + x2 = 0 + 1728 Combine like terms: 0 + 1728 = 1728 60x + x2 = 1728 The x term is 60x. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60x + 900 + x2 = 1728 + 900 Reorder the terms: 900 + 60x + x2 = 1728 + 900 Combine like terms: 1728 + 900 = 2628 900 + 60x + x2 = 2628 Factor a perfect square on the left side: (x + 30)(x + 30) = 2628 Calculate the square root of the right side: 51.264022472 Break this problem into two subproblems by setting (x + 30) equal to 51.264022472 and -51.264022472.Subproblem 1
x + 30 = 51.264022472 Simplifying x + 30 = 51.264022472 Reorder the terms: 30 + x = 51.264022472 Solving 30 + x = 51.264022472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 51.264022472 + -30 Combine like terms: 30 + -30 = 0 0 + x = 51.264022472 + -30 x = 51.264022472 + -30 Combine like terms: 51.264022472 + -30 = 21.264022472 x = 21.264022472 Simplifying x = 21.264022472Subproblem 2
x + 30 = -51.264022472 Simplifying x + 30 = -51.264022472 Reorder the terms: 30 + x = -51.264022472 Solving 30 + x = -51.264022472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = -51.264022472 + -30 Combine like terms: 30 + -30 = 0 0 + x = -51.264022472 + -30 x = -51.264022472 + -30 Combine like terms: -51.264022472 + -30 = -81.264022472 x = -81.264022472 Simplifying x = -81.264022472Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.264022472, -81.264022472}Solution
x = {21.264022472, -81.264022472}
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