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Simplifying x2 + -0.019x + -0.064 = 0 Reorder the terms: -0.064 + -0.019x + x2 = 0 Solving -0.064 + -0.019x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.064' to each side of the equation. -0.064 + -0.019x + 0.064 + x2 = 0 + 0.064 Reorder the terms: -0.064 + 0.064 + -0.019x + x2 = 0 + 0.064 Combine like terms: -0.064 + 0.064 = 0.000 0.000 + -0.019x + x2 = 0 + 0.064 -0.019x + x2 = 0 + 0.064 Combine like terms: 0 + 0.064 = 0.064 -0.019x + x2 = 0.064 The x term is -0.019x. Take half its coefficient (-0.0095). Square it (0.00009025) and add it to both sides. Add '0.00009025' to each side of the equation. -0.019x + 0.00009025 + x2 = 0.064 + 0.00009025 Reorder the terms: 0.00009025 + -0.019x + x2 = 0.064 + 0.00009025 Combine like terms: 0.064 + 0.00009025 = 0.06409025 0.00009025 + -0.019x + x2 = 0.06409025 Factor a perfect square on the left side: (x + -0.0095)(x + -0.0095) = 0.06409025 Calculate the square root of the right side: 0.253160522 Break this problem into two subproblems by setting (x + -0.0095) equal to 0.253160522 and -0.253160522.Subproblem 1
x + -0.0095 = 0.253160522 Simplifying x + -0.0095 = 0.253160522 Reorder the terms: -0.0095 + x = 0.253160522 Solving -0.0095 + x = 0.253160522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0095' to each side of the equation. -0.0095 + 0.0095 + x = 0.253160522 + 0.0095 Combine like terms: -0.0095 + 0.0095 = 0.0000 0.0000 + x = 0.253160522 + 0.0095 x = 0.253160522 + 0.0095 Combine like terms: 0.253160522 + 0.0095 = 0.262660522 x = 0.262660522 Simplifying x = 0.262660522Subproblem 2
x + -0.0095 = -0.253160522 Simplifying x + -0.0095 = -0.253160522 Reorder the terms: -0.0095 + x = -0.253160522 Solving -0.0095 + x = -0.253160522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0095' to each side of the equation. -0.0095 + 0.0095 + x = -0.253160522 + 0.0095 Combine like terms: -0.0095 + 0.0095 = 0.0000 0.0000 + x = -0.253160522 + 0.0095 x = -0.253160522 + 0.0095 Combine like terms: -0.253160522 + 0.0095 = -0.243660522 x = -0.243660522 Simplifying x = -0.243660522Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.262660522, -0.243660522}
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