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Simplifying 1016 = 2x2 + 24x Reorder the terms: 1016 = 24x + 2x2 Solving 1016 = 24x + 2x2 Solving for variable 'x'. Reorder the terms: 1016 + -24x + -2x2 = 24x + -24x + 2x2 + -2x2 Combine like terms: 24x + -24x = 0 1016 + -24x + -2x2 = 0 + 2x2 + -2x2 1016 + -24x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 1016 + -24x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(508 + -12x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(508 + -12x + -1x2)' equal to zero and attempt to solve: Simplifying 508 + -12x + -1x2 = 0 Solving 508 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -508 + 12x + x2 = 0 Move the constant term to the right: Add '508' to each side of the equation. -508 + 12x + 508 + x2 = 0 + 508 Reorder the terms: -508 + 508 + 12x + x2 = 0 + 508 Combine like terms: -508 + 508 = 0 0 + 12x + x2 = 0 + 508 12x + x2 = 0 + 508 Combine like terms: 0 + 508 = 508 12x + x2 = 508 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 508 + 36 Reorder the terms: 36 + 12x + x2 = 508 + 36 Combine like terms: 508 + 36 = 544 36 + 12x + x2 = 544 Factor a perfect square on the left side: (x + 6)(x + 6) = 544 Calculate the square root of the right side: 23.323807579 Break this problem into two subproblems by setting (x + 6) equal to 23.323807579 and -23.323807579.Subproblem 1
x + 6 = 23.323807579 Simplifying x + 6 = 23.323807579 Reorder the terms: 6 + x = 23.323807579 Solving 6 + x = 23.323807579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 23.323807579 + -6 Combine like terms: 6 + -6 = 0 0 + x = 23.323807579 + -6 x = 23.323807579 + -6 Combine like terms: 23.323807579 + -6 = 17.323807579 x = 17.323807579 Simplifying x = 17.323807579Subproblem 2
x + 6 = -23.323807579 Simplifying x + 6 = -23.323807579 Reorder the terms: 6 + x = -23.323807579 Solving 6 + x = -23.323807579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -23.323807579 + -6 Combine like terms: 6 + -6 = 0 0 + x = -23.323807579 + -6 x = -23.323807579 + -6 Combine like terms: -23.323807579 + -6 = -29.323807579 x = -29.323807579 Simplifying x = -29.323807579Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.323807579, -29.323807579}Solution
x = {17.323807579, -29.323807579}
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