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Simplifying x2 + 30x + -540 = 0 Reorder the terms: -540 + 30x + x2 = 0 Solving -540 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '540' to each side of the equation. -540 + 30x + 540 + x2 = 0 + 540 Reorder the terms: -540 + 540 + 30x + x2 = 0 + 540 Combine like terms: -540 + 540 = 0 0 + 30x + x2 = 0 + 540 30x + x2 = 0 + 540 Combine like terms: 0 + 540 = 540 30x + x2 = 540 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 540 + 225 Reorder the terms: 225 + 30x + x2 = 540 + 225 Combine like terms: 540 + 225 = 765 225 + 30x + x2 = 765 Factor a perfect square on the left side: (x + 15)(x + 15) = 765 Calculate the square root of the right side: 27.658633372 Break this problem into two subproblems by setting (x + 15) equal to 27.658633372 and -27.658633372.Subproblem 1
x + 15 = 27.658633372 Simplifying x + 15 = 27.658633372 Reorder the terms: 15 + x = 27.658633372 Solving 15 + x = 27.658633372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 27.658633372 + -15 Combine like terms: 15 + -15 = 0 0 + x = 27.658633372 + -15 x = 27.658633372 + -15 Combine like terms: 27.658633372 + -15 = 12.658633372 x = 12.658633372 Simplifying x = 12.658633372Subproblem 2
x + 15 = -27.658633372 Simplifying x + 15 = -27.658633372 Reorder the terms: 15 + x = -27.658633372 Solving 15 + x = -27.658633372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -27.658633372 + -15 Combine like terms: 15 + -15 = 0 0 + x = -27.658633372 + -15 x = -27.658633372 + -15 Combine like terms: -27.658633372 + -15 = -42.658633372 x = -42.658633372 Simplifying x = -42.658633372Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.658633372, -42.658633372}
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