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Simplifying -4.9x2 + 100x + 3 = 0 Reorder the terms: 3 + 100x + -4.9x2 = 0 Solving 3 + 100x + -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'. -0.612244898 + -20.40816327x + x2 = 0 Move the constant term to the right: Add '0.612244898' to each side of the equation. -0.612244898 + -20.40816327x + 0.612244898 + x2 = 0 + 0.612244898 Reorder the terms: -0.612244898 + 0.612244898 + -20.40816327x + x2 = 0 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + -20.40816327x + x2 = 0 + 0.612244898 -20.40816327x + x2 = 0 + 0.612244898 Combine like terms: 0 + 0.612244898 = 0.612244898 -20.40816327x + x2 = 0.612244898 The x term is -20.40816327x. Take half its coefficient (-10.20408164). Square it (104.1232821) and add it to both sides. Add '104.1232821' to each side of the equation. -20.40816327x + 104.1232821 + x2 = 0.612244898 + 104.1232821 Reorder the terms: 104.1232821 + -20.40816327x + x2 = 0.612244898 + 104.1232821 Combine like terms: 0.612244898 + 104.1232821 = 104.735526998 104.1232821 + -20.40816327x + x2 = 104.735526998 Factor a perfect square on the left side: (x + -10.20408164)(x + -10.20408164) = 104.735526998 Calculate the square root of the right side: 10.234037668 Break this problem into two subproblems by setting (x + -10.20408164) equal to 10.234037668 and -10.234037668.Subproblem 1
x + -10.20408164 = 10.234037668 Simplifying x + -10.20408164 = 10.234037668 Reorder the terms: -10.20408164 + x = 10.234037668 Solving -10.20408164 + x = 10.234037668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.20408164' to each side of the equation. -10.20408164 + 10.20408164 + x = 10.234037668 + 10.20408164 Combine like terms: -10.20408164 + 10.20408164 = 0.00000000 0.00000000 + x = 10.234037668 + 10.20408164 x = 10.234037668 + 10.20408164 Combine like terms: 10.234037668 + 10.20408164 = 20.438119308 x = 20.438119308 Simplifying x = 20.438119308Subproblem 2
x + -10.20408164 = -10.234037668 Simplifying x + -10.20408164 = -10.234037668 Reorder the terms: -10.20408164 + x = -10.234037668 Solving -10.20408164 + x = -10.234037668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.20408164' to each side of the equation. -10.20408164 + 10.20408164 + x = -10.234037668 + 10.20408164 Combine like terms: -10.20408164 + 10.20408164 = 0.00000000 0.00000000 + x = -10.234037668 + 10.20408164 x = -10.234037668 + 10.20408164 Combine like terms: -10.234037668 + 10.20408164 = -0.029956028 x = -0.029956028 Simplifying x = -0.029956028Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.438119308, -0.029956028}
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