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Simplifying 0 = -0.02x2 + 0.8x + 37 Reorder the terms: 0 = 37 + 0.8x + -0.02x2 Solving 0 = 37 + 0.8x + -0.02x2 Solving for variable 'x'. Combine like terms: 0 + -37 = -37 -37 + -0.8x + 0.02x2 = 37 + 0.8x + -0.02x2 + -37 + -0.8x + 0.02x2 Reorder the terms: -37 + -0.8x + 0.02x2 = 37 + -37 + 0.8x + -0.8x + -0.02x2 + 0.02x2 Combine like terms: 37 + -37 = 0 -37 + -0.8x + 0.02x2 = 0 + 0.8x + -0.8x + -0.02x2 + 0.02x2 -37 + -0.8x + 0.02x2 = 0.8x + -0.8x + -0.02x2 + 0.02x2 Combine like terms: 0.8x + -0.8x = 0.0 -37 + -0.8x + 0.02x2 = 0.0 + -0.02x2 + 0.02x2 -37 + -0.8x + 0.02x2 = -0.02x2 + 0.02x2 Combine like terms: -0.02x2 + 0.02x2 = 0.00 -37 + -0.8x + 0.02x2 = 0.00 Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. -1850 + -40x + x2 = 0 Move the constant term to the right: Add '1850' to each side of the equation. -1850 + -40x + 1850 + x2 = 0 + 1850 Reorder the terms: -1850 + 1850 + -40x + x2 = 0 + 1850 Combine like terms: -1850 + 1850 = 0 0 + -40x + x2 = 0 + 1850 -40x + x2 = 0 + 1850 Combine like terms: 0 + 1850 = 1850 -40x + x2 = 1850 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 = 1850 + 400 Reorder the terms: 400 + -40x + x2 = 1850 + 400 Combine like terms: 1850 + 400 = 2250 400 + -40x + x2 = 2250 Factor a perfect square on the left side: (x + -20)(x + -20) = 2250 Calculate the square root of the right side: 47.434164903 Break this problem into two subproblems by setting (x + -20) equal to 47.434164903 and -47.434164903.Subproblem 1
x + -20 = 47.434164903 Simplifying x + -20 = 47.434164903 Reorder the terms: -20 + x = 47.434164903 Solving -20 + x = 47.434164903 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 = 47.434164903 + 20 Combine like terms: -20 + 20 = 0 0 + x = 47.434164903 + 20 x = 47.434164903 + 20 Combine like terms: 47.434164903 + 20 = 67.434164903 x = 67.434164903 Simplifying x = 67.434164903Subproblem 2
x + -20 = -47.434164903 Simplifying x + -20 = -47.434164903 Reorder the terms: -20 + x = -47.434164903 Solving -20 + x = -47.434164903 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 = -47.434164903 + 20 Combine like terms: -20 + 20 = 0 0 + x = -47.434164903 + 20 x = -47.434164903 + 20 Combine like terms: -47.434164903 + 20 = -27.434164903 x = -27.434164903 Simplifying x = -27.434164903Solution
The solution to the problem is based on the solutions from the subproblems. x = {67.434164903, -27.434164903}
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