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Simplifying 28x(x + 2) = 7840 Reorder the terms: 28x(2 + x) = 7840 (2 * 28x + x * 28x) = 7840 (56x + 28x2) = 7840 Solving 56x + 28x2 = 7840 Solving for variable 'x'. Reorder the terms: -7840 + 56x + 28x2 = 7840 + -7840 Combine like terms: 7840 + -7840 = 0 -7840 + 56x + 28x2 = 0 Factor out the Greatest Common Factor (GCF), '28'. 28(-280 + 2x + x2) = 0 Ignore the factor 28.Subproblem 1
Set the factor '(-280 + 2x + x2)' equal to zero and attempt to solve: Simplifying -280 + 2x + x2 = 0 Solving -280 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '280' to each side of the equation. -280 + 2x + 280 + x2 = 0 + 280 Reorder the terms: -280 + 280 + 2x + x2 = 0 + 280 Combine like terms: -280 + 280 = 0 0 + 2x + x2 = 0 + 280 2x + x2 = 0 + 280 Combine like terms: 0 + 280 = 280 2x + x2 = 280 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 = 280 + 1 Reorder the terms: 1 + 2x + x2 = 280 + 1 Combine like terms: 280 + 1 = 281 1 + 2x + x2 = 281 Factor a perfect square on the left side: (x + 1)(x + 1) = 281 Calculate the square root of the right side: 16.763054614 Break this problem into two subproblems by setting (x + 1) equal to 16.763054614 and -16.763054614.Subproblem 1
x + 1 = 16.763054614 Simplifying x + 1 = 16.763054614 Reorder the terms: 1 + x = 16.763054614 Solving 1 + x = 16.763054614 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 = 16.763054614 + -1 Combine like terms: 1 + -1 = 0 0 + x = 16.763054614 + -1 x = 16.763054614 + -1 Combine like terms: 16.763054614 + -1 = 15.763054614 x = 15.763054614 Simplifying x = 15.763054614Subproblem 2
x + 1 = -16.763054614 Simplifying x + 1 = -16.763054614 Reorder the terms: 1 + x = -16.763054614 Solving 1 + x = -16.763054614 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 = -16.763054614 + -1 Combine like terms: 1 + -1 = 0 0 + x = -16.763054614 + -1 x = -16.763054614 + -1 Combine like terms: -16.763054614 + -1 = -17.763054614 x = -17.763054614 Simplifying x = -17.763054614Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.763054614, -17.763054614}Solution
x = {15.763054614, -17.763054614}
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