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Simplifying -2170x2 + 2x + 8 = 0 Reorder the terms: 8 + 2x + -2170x2 = 0 Solving 8 + 2x + -2170x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + x + -1085x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + x + -1085x2)' equal to zero and attempt to solve: Simplifying 4 + x + -1085x2 = 0 Solving 4 + x + -1085x2 = 0 Begin completing the square. Divide all terms by -1085 the coefficient of the squared term: Divide each side by '-1085'. -0.003686635945 + -0.0009216589862x + x2 = 0 Move the constant term to the right: Add '0.003686635945' to each side of the equation. -0.003686635945 + -0.0009216589862x + 0.003686635945 + x2 = 0 + 0.003686635945 Reorder the terms: -0.003686635945 + 0.003686635945 + -0.0009216589862x + x2 = 0 + 0.003686635945 Combine like terms: -0.003686635945 + 0.003686635945 = 0.000000000000 0.000000000000 + -0.0009216589862x + x2 = 0 + 0.003686635945 -0.0009216589862x + x2 = 0 + 0.003686635945 Combine like terms: 0 + 0.003686635945 = 0.003686635945 -0.0009216589862x + x2 = 0.003686635945 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.0009216589862x + 0.25 + x2 = 0.003686635945 + 0.25 Reorder the terms: 0.25 + -0.0009216589862x + x2 = 0.003686635945 + 0.25 Combine like terms: 0.003686635945 + 0.25 = 0.253686635945 0.25 + -0.0009216589862x + x2 = 0.253686635945 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.253686635945 Calculate the square root of the right side: 0.503673144 Break this problem into two subproblems by setting (x + 0.5) equal to 0.503673144 and -0.503673144.Subproblem 1
x + 0.5 = 0.503673144 Simplifying x + 0.5 = 0.503673144 Reorder the terms: 0.5 + x = 0.503673144 Solving 0.5 + x = 0.503673144 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.503673144 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.503673144 + -0.5 x = 0.503673144 + -0.5 Combine like terms: 0.503673144 + -0.5 = 0.003673144 x = 0.003673144 Simplifying x = 0.003673144Subproblem 2
x + 0.5 = -0.503673144 Simplifying x + 0.5 = -0.503673144 Reorder the terms: 0.5 + x = -0.503673144 Solving 0.5 + x = -0.503673144 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.503673144 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.503673144 + -0.5 x = -0.503673144 + -0.5 Combine like terms: -0.503673144 + -0.5 = -1.003673144 x = -1.003673144 Simplifying x = -1.003673144Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.003673144, -1.003673144}Solution
x = {0.003673144, -1.003673144}
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