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Simplifying 2x2 + 56x + -10 = 0 Reorder the terms: -10 + 56x + 2x2 = 0 Solving -10 + 56x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 28x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 28x + x2)' equal to zero and attempt to solve: Simplifying -5 + 28x + x2 = 0 Solving -5 + 28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 28x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 28x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 28x + x2 = 0 + 5 28x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 28x + x2 = 5 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = 5 + 196 Reorder the terms: 196 + 28x + x2 = 5 + 196 Combine like terms: 5 + 196 = 201 196 + 28x + x2 = 201 Factor a perfect square on the left side: (x + 14)(x + 14) = 201 Calculate the square root of the right side: 14.177446879 Break this problem into two subproblems by setting (x + 14) equal to 14.177446879 and -14.177446879.Subproblem 1
x + 14 = 14.177446879 Simplifying x + 14 = 14.177446879 Reorder the terms: 14 + x = 14.177446879 Solving 14 + x = 14.177446879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 14.177446879 + -14 Combine like terms: 14 + -14 = 0 0 + x = 14.177446879 + -14 x = 14.177446879 + -14 Combine like terms: 14.177446879 + -14 = 0.177446879 x = 0.177446879 Simplifying x = 0.177446879Subproblem 2
x + 14 = -14.177446879 Simplifying x + 14 = -14.177446879 Reorder the terms: 14 + x = -14.177446879 Solving 14 + x = -14.177446879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -14.177446879 + -14 Combine like terms: 14 + -14 = 0 0 + x = -14.177446879 + -14 x = -14.177446879 + -14 Combine like terms: -14.177446879 + -14 = -28.177446879 x = -28.177446879 Simplifying x = -28.177446879Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.177446879, -28.177446879}Solution
x = {0.177446879, -28.177446879}
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