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Simplifying 0 = -0.05x2 + 2x + 4 Reorder the terms: 0 = 4 + 2x + -0.05x2 Solving 0 = 4 + 2x + -0.05x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + -2x + 0.05x2 = 4 + 2x + -0.05x2 + -4 + -2x + 0.05x2 Reorder the terms: -4 + -2x + 0.05x2 = 4 + -4 + 2x + -2x + -0.05x2 + 0.05x2 Combine like terms: 4 + -4 = 0 -4 + -2x + 0.05x2 = 0 + 2x + -2x + -0.05x2 + 0.05x2 -4 + -2x + 0.05x2 = 2x + -2x + -0.05x2 + 0.05x2 Combine like terms: 2x + -2x = 0 -4 + -2x + 0.05x2 = 0 + -0.05x2 + 0.05x2 -4 + -2x + 0.05x2 = -0.05x2 + 0.05x2 Combine like terms: -0.05x2 + 0.05x2 = 0.00 -4 + -2x + 0.05x2 = 0.00 Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -80 + -40x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + -40x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + -40x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -40x + x2 = 0 + 80 -40x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 -40x + x2 = 80 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 = 80 + 400 Reorder the terms: 400 + -40x + x2 = 80 + 400 Combine like terms: 80 + 400 = 480 400 + -40x + x2 = 480 Factor a perfect square on the left side: (x + -20)(x + -20) = 480 Calculate the square root of the right side: 21.9089023 Break this problem into two subproblems by setting (x + -20) equal to 21.9089023 and -21.9089023.Subproblem 1
x + -20 = 21.9089023 Simplifying x + -20 = 21.9089023 Reorder the terms: -20 + x = 21.9089023 Solving -20 + x = 21.9089023 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 = 21.9089023 + 20 Combine like terms: -20 + 20 = 0 0 + x = 21.9089023 + 20 x = 21.9089023 + 20 Combine like terms: 21.9089023 + 20 = 41.9089023 x = 41.9089023 Simplifying x = 41.9089023Subproblem 2
x + -20 = -21.9089023 Simplifying x + -20 = -21.9089023 Reorder the terms: -20 + x = -21.9089023 Solving -20 + x = -21.9089023 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 = -21.9089023 + 20 Combine like terms: -20 + 20 = 0 0 + x = -21.9089023 + 20 x = -21.9089023 + 20 Combine like terms: -21.9089023 + 20 = -1.9089023 x = -1.9089023 Simplifying x = -1.9089023Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.9089023, -1.9089023}
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