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Simplifying -0.02x2 + 1.2x + 0.605 = 5.085 Reorder the terms: 0.605 + 1.2x + -0.02x2 = 5.085 Solving 0.605 + 1.2x + -0.02x2 = 5.085 Solving for variable 'x'. Reorder the terms: 0.605 + -5.085 + 1.2x + -0.02x2 = 5.085 + -5.085 Combine like terms: 0.605 + -5.085 = -4.48 -4.48 + 1.2x + -0.02x2 = 5.085 + -5.085 Combine like terms: 5.085 + -5.085 = 0.000 -4.48 + 1.2x + -0.02x2 = 0.000 Begin completing the square. Divide all terms by -0.02 the coefficient of the squared term: Divide each side by '-0.02'. 224 + -60x + x2 = 0.0 Move the constant term to the right: Add '-224' to each side of the equation. 224 + -60x + -224 + x2 = 0.0 + -224 Reorder the terms: 224 + -224 + -60x + x2 = 0.0 + -224 Combine like terms: 224 + -224 = 0 0 + -60x + x2 = 0.0 + -224 -60x + x2 = 0.0 + -224 Combine like terms: 0.0 + -224 = -224 -60x + x2 = -224 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 = -224 + 900 Reorder the terms: 900 + -60x + x2 = -224 + 900 Combine like terms: -224 + 900 = 676 900 + -60x + x2 = 676 Factor a perfect square on the left side: (x + -30)(x + -30) = 676 Calculate the square root of the right side: 26 Break this problem into two subproblems by setting (x + -30) equal to 26 and -26.Subproblem 1
x + -30 = 26 Simplifying x + -30 = 26 Reorder the terms: -30 + x = 26 Solving -30 + x = 26 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 = 26 + 30 Combine like terms: -30 + 30 = 0 0 + x = 26 + 30 x = 26 + 30 Combine like terms: 26 + 30 = 56 x = 56 Simplifying x = 56Subproblem 2
x + -30 = -26 Simplifying x + -30 = -26 Reorder the terms: -30 + x = -26 Solving -30 + x = -26 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 = -26 + 30 Combine like terms: -30 + 30 = 0 0 + x = -26 + 30 x = -26 + 30 Combine like terms: -26 + 30 = 4 x = 4 Simplifying x = 4Solution
The solution to the problem is based on the solutions from the subproblems. x = {56, 4}
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