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Simplifying 0.02x2 + -3.4x + 16 = 0 Reorder the terms: 16 + -3.4x + 0.02x2 = 0 Solving 16 + -3.4x + 0.02x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. 800 + -170x + x2 = 0 Move the constant term to the right: Add '-800' to each side of the equation. 800 + -170x + -800 + x2 = 0 + -800 Reorder the terms: 800 + -800 + -170x + x2 = 0 + -800 Combine like terms: 800 + -800 = 0 0 + -170x + x2 = 0 + -800 -170x + x2 = 0 + -800 Combine like terms: 0 + -800 = -800 -170x + x2 = -800 The x term is -170x. Take half its coefficient (-85). Square it (7225) and add it to both sides. Add '7225' to each side of the equation. -170x + 7225 + x2 = -800 + 7225 Reorder the terms: 7225 + -170x + x2 = -800 + 7225 Combine like terms: -800 + 7225 = 6425 7225 + -170x + x2 = 6425 Factor a perfect square on the left side: (x + -85)(x + -85) = 6425 Calculate the square root of the right side: 80.156097709 Break this problem into two subproblems by setting (x + -85) equal to 80.156097709 and -80.156097709.Subproblem 1
x + -85 = 80.156097709 Simplifying x + -85 = 80.156097709 Reorder the terms: -85 + x = 80.156097709 Solving -85 + x = 80.156097709 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '85' to each side of the equation. -85 + 85 + x = 80.156097709 + 85 Combine like terms: -85 + 85 = 0 0 + x = 80.156097709 + 85 x = 80.156097709 + 85 Combine like terms: 80.156097709 + 85 = 165.156097709 x = 165.156097709 Simplifying x = 165.156097709Subproblem 2
x + -85 = -80.156097709 Simplifying x + -85 = -80.156097709 Reorder the terms: -85 + x = -80.156097709 Solving -85 + x = -80.156097709 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '85' to each side of the equation. -85 + 85 + x = -80.156097709 + 85 Combine like terms: -85 + 85 = 0 0 + x = -80.156097709 + 85 x = -80.156097709 + 85 Combine like terms: -80.156097709 + 85 = 4.843902291 x = 4.843902291 Simplifying x = 4.843902291Solution
The solution to the problem is based on the solutions from the subproblems. x = {165.156097709, 4.843902291}
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