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Simplifying -0.02x2 + 1.4x + -12 = 0 Reorder the terms: -12 + 1.4x + -0.02x2 = 0 Solving -12 + 1.4x + -0.02x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.02 the coefficient of the squared term: Divide each side by '-0.02'. 600 + -70x + x2 = 0 Move the constant term to the right: Add '-600' to each side of the equation. 600 + -70x + -600 + x2 = 0 + -600 Reorder the terms: 600 + -600 + -70x + x2 = 0 + -600 Combine like terms: 600 + -600 = 0 0 + -70x + x2 = 0 + -600 -70x + x2 = 0 + -600 Combine like terms: 0 + -600 = -600 -70x + x2 = -600 The x term is -70x. Take half its coefficient (-35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. -70x + 1225 + x2 = -600 + 1225 Reorder the terms: 1225 + -70x + x2 = -600 + 1225 Combine like terms: -600 + 1225 = 625 1225 + -70x + x2 = 625 Factor a perfect square on the left side: (x + -35)(x + -35) = 625 Calculate the square root of the right side: 25 Break this problem into two subproblems by setting (x + -35) equal to 25 and -25.Subproblem 1
x + -35 = 25 Simplifying x + -35 = 25 Reorder the terms: -35 + x = 25 Solving -35 + x = 25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = 25 + 35 Combine like terms: -35 + 35 = 0 0 + x = 25 + 35 x = 25 + 35 Combine like terms: 25 + 35 = 60 x = 60 Simplifying x = 60Subproblem 2
x + -35 = -25 Simplifying x + -35 = -25 Reorder the terms: -35 + x = -25 Solving -35 + x = -25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = -25 + 35 Combine like terms: -35 + 35 = 0 0 + x = -25 + 35 x = -25 + 35 Combine like terms: -25 + 35 = 10 x = 10 Simplifying x = 10Solution
The solution to the problem is based on the solutions from the subproblems. x = {60, 10}
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