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Simplifying 63 + 0.2x + -0.01x2 = 0 Solving 63 + 0.2x + -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'. -6300 + -20x + x2 = 0 Move the constant term to the right: Add '6300' to each side of the equation. -6300 + -20x + 6300 + x2 = 0 + 6300 Reorder the terms: -6300 + 6300 + -20x + x2 = 0 + 6300 Combine like terms: -6300 + 6300 = 0 0 + -20x + x2 = 0 + 6300 -20x + x2 = 0 + 6300 Combine like terms: 0 + 6300 = 6300 -20x + x2 = 6300 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 6300 + 100 Reorder the terms: 100 + -20x + x2 = 6300 + 100 Combine like terms: 6300 + 100 = 6400 100 + -20x + x2 = 6400 Factor a perfect square on the left side: (x + -10)(x + -10) = 6400 Calculate the square root of the right side: 80 Break this problem into two subproblems by setting (x + -10) equal to 80 and -80.Subproblem 1
x + -10 = 80 Simplifying x + -10 = 80 Reorder the terms: -10 + x = 80 Solving -10 + x = 80 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 80 + 10 Combine like terms: -10 + 10 = 0 0 + x = 80 + 10 x = 80 + 10 Combine like terms: 80 + 10 = 90 x = 90 Simplifying x = 90Subproblem 2
x + -10 = -80 Simplifying x + -10 = -80 Reorder the terms: -10 + x = -80 Solving -10 + x = -80 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -80 + 10 Combine like terms: -10 + 10 = 0 0 + x = -80 + 10 x = -80 + 10 Combine like terms: -80 + 10 = -70 x = -70 Simplifying x = -70Solution
The solution to the problem is based on the solutions from the subproblems. x = {90, -70}
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