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Simplifying -0.02x2 + 1x + 6.1 = 0 Reorder the terms: 6.1 + 1x + -0.02x2 = 0 Solving 6.1 + 1x + -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'. -305 + -50x + x2 = 0 Move the constant term to the right: Add '305' to each side of the equation. -305 + -50x + 305 + x2 = 0 + 305 Reorder the terms: -305 + 305 + -50x + x2 = 0 + 305 Combine like terms: -305 + 305 = 0 0 + -50x + x2 = 0 + 305 -50x + x2 = 0 + 305 Combine like terms: 0 + 305 = 305 -50x + x2 = 305 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = 305 + 625 Reorder the terms: 625 + -50x + x2 = 305 + 625 Combine like terms: 305 + 625 = 930 625 + -50x + x2 = 930 Factor a perfect square on the left side: (x + -25)(x + -25) = 930 Calculate the square root of the right side: 30.495901364 Break this problem into two subproblems by setting (x + -25) equal to 30.495901364 and -30.495901364.Subproblem 1
x + -25 = 30.495901364 Simplifying x + -25 = 30.495901364 Reorder the terms: -25 + x = 30.495901364 Solving -25 + x = 30.495901364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 30.495901364 + 25 Combine like terms: -25 + 25 = 0 0 + x = 30.495901364 + 25 x = 30.495901364 + 25 Combine like terms: 30.495901364 + 25 = 55.495901364 x = 55.495901364 Simplifying x = 55.495901364Subproblem 2
x + -25 = -30.495901364 Simplifying x + -25 = -30.495901364 Reorder the terms: -25 + x = -30.495901364 Solving -25 + x = -30.495901364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -30.495901364 + 25 Combine like terms: -25 + 25 = 0 0 + x = -30.495901364 + 25 x = -30.495901364 + 25 Combine like terms: -30.495901364 + 25 = -5.495901364 x = -5.495901364 Simplifying x = -5.495901364Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.495901364, -5.495901364}
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