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Simplifying 0 = -0.04x2 + 0.84x + 2 Reorder the terms: 0 = 2 + 0.84x + -0.04x2 Solving 0 = 2 + 0.84x + -0.04x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + -0.84x + 0.04x2 = 2 + 0.84x + -0.04x2 + -2 + -0.84x + 0.04x2 Reorder the terms: -2 + -0.84x + 0.04x2 = 2 + -2 + 0.84x + -0.84x + -0.04x2 + 0.04x2 Combine like terms: 2 + -2 = 0 -2 + -0.84x + 0.04x2 = 0 + 0.84x + -0.84x + -0.04x2 + 0.04x2 -2 + -0.84x + 0.04x2 = 0.84x + -0.84x + -0.04x2 + 0.04x2 Combine like terms: 0.84x + -0.84x = 0.00 -2 + -0.84x + 0.04x2 = 0.00 + -0.04x2 + 0.04x2 -2 + -0.84x + 0.04x2 = -0.04x2 + 0.04x2 Combine like terms: -0.04x2 + 0.04x2 = 0.00 -2 + -0.84x + 0.04x2 = 0.00 Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. -50 + -21x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -21x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -21x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -21x + x2 = 0 + 50 -21x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -21x + x2 = 50 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = 50 + 110.25 Reorder the terms: 110.25 + -21x + x2 = 50 + 110.25 Combine like terms: 50 + 110.25 = 160.25 110.25 + -21x + x2 = 160.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 160.25 Calculate the square root of the right side: 12.658988901 Break this problem into two subproblems by setting (x + -10.5) equal to 12.658988901 and -12.658988901.Subproblem 1
x + -10.5 = 12.658988901 Simplifying x + -10.5 = 12.658988901 Reorder the terms: -10.5 + x = 12.658988901 Solving -10.5 + x = 12.658988901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 12.658988901 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 12.658988901 + 10.5 x = 12.658988901 + 10.5 Combine like terms: 12.658988901 + 10.5 = 23.158988901 x = 23.158988901 Simplifying x = 23.158988901Subproblem 2
x + -10.5 = -12.658988901 Simplifying x + -10.5 = -12.658988901 Reorder the terms: -10.5 + x = -12.658988901 Solving -10.5 + x = -12.658988901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -12.658988901 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -12.658988901 + 10.5 x = -12.658988901 + 10.5 Combine like terms: -12.658988901 + 10.5 = -2.158988901 x = -2.158988901 Simplifying x = -2.158988901Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.158988901, -2.158988901}
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