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Simplifying (2x2) + 28x = 4624 Reorder the terms: 28x + (2x2) = 4624 Solving 28x + (2x2) = 4624 Solving for variable 'x'. Reorder the terms: -4624 + 28x + (2x2) = 4624 + -4624 Combine like terms: 4624 + -4624 = 0 -4624 + 28x + (2x2) = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2312 + 14x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2312 + 14x + x2)' equal to zero and attempt to solve: Simplifying -2312 + 14x + x2 = 0 Solving -2312 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2312' to each side of the equation. -2312 + 14x + 2312 + x2 = 0 + 2312 Reorder the terms: -2312 + 2312 + 14x + x2 = 0 + 2312 Combine like terms: -2312 + 2312 = 0 0 + 14x + x2 = 0 + 2312 14x + x2 = 0 + 2312 Combine like terms: 0 + 2312 = 2312 14x + x2 = 2312 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 2312 + 49 Reorder the terms: 49 + 14x + x2 = 2312 + 49 Combine like terms: 2312 + 49 = 2361 49 + 14x + x2 = 2361 Factor a perfect square on the left side: (x + 7)(x + 7) = 2361 Calculate the square root of the right side: 48.590122453 Break this problem into two subproblems by setting (x + 7) equal to 48.590122453 and -48.590122453.Subproblem 1
x + 7 = 48.590122453 Simplifying x + 7 = 48.590122453 Reorder the terms: 7 + x = 48.590122453 Solving 7 + x = 48.590122453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 48.590122453 + -7 Combine like terms: 7 + -7 = 0 0 + x = 48.590122453 + -7 x = 48.590122453 + -7 Combine like terms: 48.590122453 + -7 = 41.590122453 x = 41.590122453 Simplifying x = 41.590122453Subproblem 2
x + 7 = -48.590122453 Simplifying x + 7 = -48.590122453 Reorder the terms: 7 + x = -48.590122453 Solving 7 + x = -48.590122453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -48.590122453 + -7 Combine like terms: 7 + -7 = 0 0 + x = -48.590122453 + -7 x = -48.590122453 + -7 Combine like terms: -48.590122453 + -7 = -55.590122453 x = -55.590122453 Simplifying x = -55.590122453Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.590122453, -55.590122453}Solution
x = {41.590122453, -55.590122453}
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