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Simplifying 180 = 24x + -0.4x2 Solving 180 = 24x + -0.4x2 Solving for variable 'x'. Reorder the terms: 180 + -24x + 0.4x2 = 24x + -24x + -0.4x2 + 0.4x2 Combine like terms: 24x + -24x = 0 180 + -24x + 0.4x2 = 0 + -0.4x2 + 0.4x2 180 + -24x + 0.4x2 = -0.4x2 + 0.4x2 Combine like terms: -0.4x2 + 0.4x2 = 0.0 180 + -24x + 0.4x2 = 0.0 Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. 450 + -60x + x2 = 0 Move the constant term to the right: Add '-450' to each side of the equation. 450 + -60x + -450 + x2 = 0 + -450 Reorder the terms: 450 + -450 + -60x + x2 = 0 + -450 Combine like terms: 450 + -450 = 0 0 + -60x + x2 = 0 + -450 -60x + x2 = 0 + -450 Combine like terms: 0 + -450 = -450 -60x + x2 = -450 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = -450 + 900 Reorder the terms: 900 + -60x + x2 = -450 + 900 Combine like terms: -450 + 900 = 450 900 + -60x + x2 = 450 Factor a perfect square on the left side: (x + -30)(x + -30) = 450 Calculate the square root of the right side: 21.213203436 Break this problem into two subproblems by setting (x + -30) equal to 21.213203436 and -21.213203436.Subproblem 1
x + -30 = 21.213203436 Simplifying x + -30 = 21.213203436 Reorder the terms: -30 + x = 21.213203436 Solving -30 + x = 21.213203436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 21.213203436 + 30 Combine like terms: -30 + 30 = 0 0 + x = 21.213203436 + 30 x = 21.213203436 + 30 Combine like terms: 21.213203436 + 30 = 51.213203436 x = 51.213203436 Simplifying x = 51.213203436Subproblem 2
x + -30 = -21.213203436 Simplifying x + -30 = -21.213203436 Reorder the terms: -30 + x = -21.213203436 Solving -30 + x = -21.213203436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -21.213203436 + 30 Combine like terms: -30 + 30 = 0 0 + x = -21.213203436 + 30 x = -21.213203436 + 30 Combine like terms: -21.213203436 + 30 = 8.786796564 x = 8.786796564 Simplifying x = 8.786796564Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.213203436, 8.786796564}
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