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Simplifying -0.01x2 + 0.28x + 8.68 = 0 Reorder the terms: 8.68 + 0.28x + -0.01x2 = 0 Solving 8.68 + 0.28x + -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'. -868 + -28x + x2 = 0 Move the constant term to the right: Add '868' to each side of the equation. -868 + -28x + 868 + x2 = 0 + 868 Reorder the terms: -868 + 868 + -28x + x2 = 0 + 868 Combine like terms: -868 + 868 = 0 0 + -28x + x2 = 0 + 868 -28x + x2 = 0 + 868 Combine like terms: 0 + 868 = 868 -28x + x2 = 868 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = 868 + 196 Reorder the terms: 196 + -28x + x2 = 868 + 196 Combine like terms: 868 + 196 = 1064 196 + -28x + x2 = 1064 Factor a perfect square on the left side: (x + -14)(x + -14) = 1064 Calculate the square root of the right side: 32.619012861 Break this problem into two subproblems by setting (x + -14) equal to 32.619012861 and -32.619012861.Subproblem 1
x + -14 = 32.619012861 Simplifying x + -14 = 32.619012861 Reorder the terms: -14 + x = 32.619012861 Solving -14 + x = 32.619012861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 32.619012861 + 14 Combine like terms: -14 + 14 = 0 0 + x = 32.619012861 + 14 x = 32.619012861 + 14 Combine like terms: 32.619012861 + 14 = 46.619012861 x = 46.619012861 Simplifying x = 46.619012861Subproblem 2
x + -14 = -32.619012861 Simplifying x + -14 = -32.619012861 Reorder the terms: -14 + x = -32.619012861 Solving -14 + x = -32.619012861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -32.619012861 + 14 Combine like terms: -14 + 14 = 0 0 + x = -32.619012861 + 14 x = -32.619012861 + 14 Combine like terms: -32.619012861 + 14 = -18.619012861 x = -18.619012861 Simplifying x = -18.619012861Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.619012861, -18.619012861}
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