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Simplifying -0.01x2 + 0.4x + 6.2 = 0 Reorder the terms: 6.2 + 0.4x + -0.01x2 = 0 Solving 6.2 + 0.4x + -0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -620 + -40x + x2 = 0 Move the constant term to the right: Add '620' to each side of the equation. -620 + -40x + 620 + x2 = 0 + 620 Reorder the terms: -620 + 620 + -40x + x2 = 0 + 620 Combine like terms: -620 + 620 = 0 0 + -40x + x2 = 0 + 620 -40x + x2 = 0 + 620 Combine like terms: 0 + 620 = 620 -40x + x2 = 620 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = 620 + 400 Reorder the terms: 400 + -40x + x2 = 620 + 400 Combine like terms: 620 + 400 = 1020 400 + -40x + x2 = 1020 Factor a perfect square on the left side: (x + -20)(x + -20) = 1020 Calculate the square root of the right side: 31.937438845 Break this problem into two subproblems by setting (x + -20) equal to 31.937438845 and -31.937438845.Subproblem 1
x + -20 = 31.937438845 Simplifying x + -20 = 31.937438845 Reorder the terms: -20 + x = 31.937438845 Solving -20 + x = 31.937438845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 31.937438845 + 20 Combine like terms: -20 + 20 = 0 0 + x = 31.937438845 + 20 x = 31.937438845 + 20 Combine like terms: 31.937438845 + 20 = 51.937438845 x = 51.937438845 Simplifying x = 51.937438845Subproblem 2
x + -20 = -31.937438845 Simplifying x + -20 = -31.937438845 Reorder the terms: -20 + x = -31.937438845 Solving -20 + x = -31.937438845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -31.937438845 + 20 Combine like terms: -20 + 20 = 0 0 + x = -31.937438845 + 20 x = -31.937438845 + 20 Combine like terms: -31.937438845 + 20 = -11.937438845 x = -11.937438845 Simplifying x = -11.937438845Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.937438845, -11.937438845}
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