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Simplifying -4.9x2 + 0.01x + 0.1 = 0 Reorder the terms: 0.1 + 0.01x + -4.9x2 = 0 Solving 0.1 + 0.01x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -0.02040816327 + -0.002040816327x + x2 = 0 Move the constant term to the right: Add '0.02040816327' to each side of the equation. -0.02040816327 + -0.002040816327x + 0.02040816327 + x2 = 0 + 0.02040816327 Reorder the terms: -0.02040816327 + 0.02040816327 + -0.002040816327x + x2 = 0 + 0.02040816327 Combine like terms: -0.02040816327 + 0.02040816327 = 0.00000000000 0.00000000000 + -0.002040816327x + x2 = 0 + 0.02040816327 -0.002040816327x + x2 = 0 + 0.02040816327 Combine like terms: 0 + 0.02040816327 = 0.02040816327 -0.002040816327x + x2 = 0.02040816327 The x term is -0.002040816327x. Take half its coefficient (-0.001020408164). Square it (0.000001041232821) and add it to both sides. Add '0.000001041232821' to each side of the equation. -0.002040816327x + 0.000001041232821 + x2 = 0.02040816327 + 0.000001041232821 Reorder the terms: 0.000001041232821 + -0.002040816327x + x2 = 0.02040816327 + 0.000001041232821 Combine like terms: 0.02040816327 + 0.000001041232821 = 0.020409204502821 0.000001041232821 + -0.002040816327x + x2 = 0.020409204502821 Factor a perfect square on the left side: (x + -0.001020408164)(x + -0.001020408164) = 0.020409204502821 Calculate the square root of the right side: 0.142860787 Break this problem into two subproblems by setting (x + -0.001020408164) equal to 0.142860787 and -0.142860787.Subproblem 1
x + -0.001020408164 = 0.142860787 Simplifying x + -0.001020408164 = 0.142860787 Reorder the terms: -0.001020408164 + x = 0.142860787 Solving -0.001020408164 + x = 0.142860787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.001020408164' to each side of the equation. -0.001020408164 + 0.001020408164 + x = 0.142860787 + 0.001020408164 Combine like terms: -0.001020408164 + 0.001020408164 = 0.000000000000 0.000000000000 + x = 0.142860787 + 0.001020408164 x = 0.142860787 + 0.001020408164 Combine like terms: 0.142860787 + 0.001020408164 = 0.143881195164 x = 0.143881195164 Simplifying x = 0.143881195164Subproblem 2
x + -0.001020408164 = -0.142860787 Simplifying x + -0.001020408164 = -0.142860787 Reorder the terms: -0.001020408164 + x = -0.142860787 Solving -0.001020408164 + x = -0.142860787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.001020408164' to each side of the equation. -0.001020408164 + 0.001020408164 + x = -0.142860787 + 0.001020408164 Combine like terms: -0.001020408164 + 0.001020408164 = 0.000000000000 0.000000000000 + x = -0.142860787 + 0.001020408164 x = -0.142860787 + 0.001020408164 Combine like terms: -0.142860787 + 0.001020408164 = -0.141840378836 x = -0.141840378836 Simplifying x = -0.141840378836Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.143881195164, -0.141840378836}
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