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Simplifying 2x + 50x2 = 35 Solving 2x + 50x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + 2x + 50x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 2x + 50x2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -0.7 + 0.04x + x2 = 0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + 0.04x + 0.7 + x2 = 0 + 0.7 Reorder the terms: -0.7 + 0.7 + 0.04x + x2 = 0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + 0.04x + x2 = 0 + 0.7 0.04x + x2 = 0 + 0.7 Combine like terms: 0 + 0.7 = 0.7 0.04x + x2 = 0.7 The x term is 0.04x. Take half its coefficient (0.02). Square it (0.0004) and add it to both sides. Add '0.0004' to each side of the equation. 0.04x + 0.0004 + x2 = 0.7 + 0.0004 Reorder the terms: 0.0004 + 0.04x + x2 = 0.7 + 0.0004 Combine like terms: 0.7 + 0.0004 = 0.7004 0.0004 + 0.04x + x2 = 0.7004 Factor a perfect square on the left side: (x + 0.02)(x + 0.02) = 0.7004 Calculate the square root of the right side: 0.836899038 Break this problem into two subproblems by setting (x + 0.02) equal to 0.836899038 and -0.836899038.Subproblem 1
x + 0.02 = 0.836899038 Simplifying x + 0.02 = 0.836899038 Reorder the terms: 0.02 + x = 0.836899038 Solving 0.02 + x = 0.836899038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02' to each side of the equation. 0.02 + -0.02 + x = 0.836899038 + -0.02 Combine like terms: 0.02 + -0.02 = 0.00 0.00 + x = 0.836899038 + -0.02 x = 0.836899038 + -0.02 Combine like terms: 0.836899038 + -0.02 = 0.816899038 x = 0.816899038 Simplifying x = 0.816899038Subproblem 2
x + 0.02 = -0.836899038 Simplifying x + 0.02 = -0.836899038 Reorder the terms: 0.02 + x = -0.836899038 Solving 0.02 + x = -0.836899038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02' to each side of the equation. 0.02 + -0.02 + x = -0.836899038 + -0.02 Combine like terms: 0.02 + -0.02 = 0.00 0.00 + x = -0.836899038 + -0.02 x = -0.836899038 + -0.02 Combine like terms: -0.836899038 + -0.02 = -0.856899038 x = -0.856899038 Simplifying x = -0.856899038Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.816899038, -0.856899038}
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