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Simplifying 2x(x + 2) = 1020 Reorder the terms: 2x(2 + x) = 1020 (2 * 2x + x * 2x) = 1020 (4x + 2x2) = 1020 Solving 4x + 2x2 = 1020 Solving for variable 'x'. Reorder the terms: -1020 + 4x + 2x2 = 1020 + -1020 Combine like terms: 1020 + -1020 = 0 -1020 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-510 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-510 + 2x + x2)' equal to zero and attempt to solve: Simplifying -510 + 2x + x2 = 0 Solving -510 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '510' to each side of the equation. -510 + 2x + 510 + x2 = 0 + 510 Reorder the terms: -510 + 510 + 2x + x2 = 0 + 510 Combine like terms: -510 + 510 = 0 0 + 2x + x2 = 0 + 510 2x + x2 = 0 + 510 Combine like terms: 0 + 510 = 510 2x + x2 = 510 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 510 + 1 Reorder the terms: 1 + 2x + x2 = 510 + 1 Combine like terms: 510 + 1 = 511 1 + 2x + x2 = 511 Factor a perfect square on the left side: (x + 1)(x + 1) = 511 Calculate the square root of the right side: 22.605309111 Break this problem into two subproblems by setting (x + 1) equal to 22.605309111 and -22.605309111.Subproblem 1
x + 1 = 22.605309111 Simplifying x + 1 = 22.605309111 Reorder the terms: 1 + x = 22.605309111 Solving 1 + x = 22.605309111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 22.605309111 + -1 Combine like terms: 1 + -1 = 0 0 + x = 22.605309111 + -1 x = 22.605309111 + -1 Combine like terms: 22.605309111 + -1 = 21.605309111 x = 21.605309111 Simplifying x = 21.605309111Subproblem 2
x + 1 = -22.605309111 Simplifying x + 1 = -22.605309111 Reorder the terms: 1 + x = -22.605309111 Solving 1 + x = -22.605309111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -22.605309111 + -1 Combine like terms: 1 + -1 = 0 0 + x = -22.605309111 + -1 x = -22.605309111 + -1 Combine like terms: -22.605309111 + -1 = -23.605309111 x = -23.605309111 Simplifying x = -23.605309111Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.605309111, -23.605309111}Solution
x = {21.605309111, -23.605309111}
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