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Simplifying 0 = 0.02x2 + 1.2x + -14 Reorder the terms: 0 = -14 + 1.2x + 0.02x2 Solving 0 = -14 + 1.2x + 0.02x2 Solving for variable 'x'. Combine like terms: 0 + 14 = 14 14 + -1.2x + -0.02x2 = -14 + 1.2x + 0.02x2 + 14 + -1.2x + -0.02x2 Reorder the terms: 14 + -1.2x + -0.02x2 = -14 + 14 + 1.2x + -1.2x + 0.02x2 + -0.02x2 Combine like terms: -14 + 14 = 0 14 + -1.2x + -0.02x2 = 0 + 1.2x + -1.2x + 0.02x2 + -0.02x2 14 + -1.2x + -0.02x2 = 1.2x + -1.2x + 0.02x2 + -0.02x2 Combine like terms: 1.2x + -1.2x = 0.0 14 + -1.2x + -0.02x2 = 0.0 + 0.02x2 + -0.02x2 14 + -1.2x + -0.02x2 = 0.02x2 + -0.02x2 Combine like terms: 0.02x2 + -0.02x2 = 0.00 14 + -1.2x + -0.02x2 = 0.00 Begin completing the square. Divide all terms by -0.02 the coefficient of the squared term: Divide each side by '-0.02'. -700 + 60x + x2 = 0 Move the constant term to the right: Add '700' to each side of the equation. -700 + 60x + 700 + x2 = 0 + 700 Reorder the terms: -700 + 700 + 60x + x2 = 0 + 700 Combine like terms: -700 + 700 = 0 0 + 60x + x2 = 0 + 700 60x + x2 = 0 + 700 Combine like terms: 0 + 700 = 700 60x + x2 = 700 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 = 700 + 900 Reorder the terms: 900 + 60x + x2 = 700 + 900 Combine like terms: 700 + 900 = 1600 900 + 60x + x2 = 1600 Factor a perfect square on the left side: (x + 30)(x + 30) = 1600 Calculate the square root of the right side: 40 Break this problem into two subproblems by setting (x + 30) equal to 40 and -40.Subproblem 1
x + 30 = 40 Simplifying x + 30 = 40 Reorder the terms: 30 + x = 40 Solving 30 + x = 40 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 = 40 + -30 Combine like terms: 30 + -30 = 0 0 + x = 40 + -30 x = 40 + -30 Combine like terms: 40 + -30 = 10 x = 10 Simplifying x = 10Subproblem 2
x + 30 = -40 Simplifying x + 30 = -40 Reorder the terms: 30 + x = -40 Solving 30 + x = -40 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 = -40 + -30 Combine like terms: 30 + -30 = 0 0 + x = -40 + -30 x = -40 + -30 Combine like terms: -40 + -30 = -70 x = -70 Simplifying x = -70Solution
The solution to the problem is based on the solutions from the subproblems. x = {10, -70}
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