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Simplifying 3 = 0.014x2 + -1.19x + 28.24 Reorder the terms: 3 = 28.24 + -1.19x + 0.014x2 Solving 3 = 28.24 + -1.19x + 0.014x2 Solving for variable 'x'. Combine like terms: 3 + -28.24 = -25.24 -25.24 + 1.19x + -0.014x2 = 28.24 + -1.19x + 0.014x2 + -28.24 + 1.19x + -0.014x2 Reorder the terms: -25.24 + 1.19x + -0.014x2 = 28.24 + -28.24 + -1.19x + 1.19x + 0.014x2 + -0.014x2 Combine like terms: 28.24 + -28.24 = 0.00 -25.24 + 1.19x + -0.014x2 = 0.00 + -1.19x + 1.19x + 0.014x2 + -0.014x2 -25.24 + 1.19x + -0.014x2 = -1.19x + 1.19x + 0.014x2 + -0.014x2 Combine like terms: -1.19x + 1.19x = 0.00 -25.24 + 1.19x + -0.014x2 = 0.00 + 0.014x2 + -0.014x2 -25.24 + 1.19x + -0.014x2 = 0.014x2 + -0.014x2 Combine like terms: 0.014x2 + -0.014x2 = 0.000 -25.24 + 1.19x + -0.014x2 = 0.000 Begin completing the square. Divide all terms by -0.014 the coefficient of the squared term: Divide each side by '-0.014'. 1802.857143 + -85x + x2 = 0 Move the constant term to the right: Add '-1802.857143' to each side of the equation. 1802.857143 + -85x + -1802.857143 + x2 = 0 + -1802.857143 Reorder the terms: 1802.857143 + -1802.857143 + -85x + x2 = 0 + -1802.857143 Combine like terms: 1802.857143 + -1802.857143 = 0.000000 0.000000 + -85x + x2 = 0 + -1802.857143 -85x + x2 = 0 + -1802.857143 Combine like terms: 0 + -1802.857143 = -1802.857143 -85x + x2 = -1802.857143 The x term is -85x. Take half its coefficient (-42.5). Square it (1806.25) and add it to both sides. Add '1806.25' to each side of the equation. -85x + 1806.25 + x2 = -1802.857143 + 1806.25 Reorder the terms: 1806.25 + -85x + x2 = -1802.857143 + 1806.25 Combine like terms: -1802.857143 + 1806.25 = 3.392857 1806.25 + -85x + x2 = 3.392857 Factor a perfect square on the left side: (x + -42.5)(x + -42.5) = 3.392857 Calculate the square root of the right side: 1.841970955 Break this problem into two subproblems by setting (x + -42.5) equal to 1.841970955 and -1.841970955.Subproblem 1
x + -42.5 = 1.841970955 Simplifying x + -42.5 = 1.841970955 Reorder the terms: -42.5 + x = 1.841970955 Solving -42.5 + x = 1.841970955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42.5' to each side of the equation. -42.5 + 42.5 + x = 1.841970955 + 42.5 Combine like terms: -42.5 + 42.5 = 0.0 0.0 + x = 1.841970955 + 42.5 x = 1.841970955 + 42.5 Combine like terms: 1.841970955 + 42.5 = 44.341970955 x = 44.341970955 Simplifying x = 44.341970955Subproblem 2
x + -42.5 = -1.841970955 Simplifying x + -42.5 = -1.841970955 Reorder the terms: -42.5 + x = -1.841970955 Solving -42.5 + x = -1.841970955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42.5' to each side of the equation. -42.5 + 42.5 + x = -1.841970955 + 42.5 Combine like terms: -42.5 + 42.5 = 0.0 0.0 + x = -1.841970955 + 42.5 x = -1.841970955 + 42.5 Combine like terms: -1.841970955 + 42.5 = 40.658029045 x = 40.658029045 Simplifying x = 40.658029045Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.341970955, 40.658029045}
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