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Simplifying 0 = -0.02x2 + 2.6x + -66.5 Reorder the terms: 0 = -66.5 + 2.6x + -0.02x2 Solving 0 = -66.5 + 2.6x + -0.02x2 Solving for variable 'x'. Combine like terms: 0 + 66.5 = 66.5 66.5 + -2.6x + 0.02x2 = -66.5 + 2.6x + -0.02x2 + 66.5 + -2.6x + 0.02x2 Reorder the terms: 66.5 + -2.6x + 0.02x2 = -66.5 + 66.5 + 2.6x + -2.6x + -0.02x2 + 0.02x2 Combine like terms: -66.5 + 66.5 = 0.0 66.5 + -2.6x + 0.02x2 = 0.0 + 2.6x + -2.6x + -0.02x2 + 0.02x2 66.5 + -2.6x + 0.02x2 = 2.6x + -2.6x + -0.02x2 + 0.02x2 Combine like terms: 2.6x + -2.6x = 0.0 66.5 + -2.6x + 0.02x2 = 0.0 + -0.02x2 + 0.02x2 66.5 + -2.6x + 0.02x2 = -0.02x2 + 0.02x2 Combine like terms: -0.02x2 + 0.02x2 = 0.00 66.5 + -2.6x + 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'. 3325 + -130x + x2 = 0 Move the constant term to the right: Add '-3325' to each side of the equation. 3325 + -130x + -3325 + x2 = 0 + -3325 Reorder the terms: 3325 + -3325 + -130x + x2 = 0 + -3325 Combine like terms: 3325 + -3325 = 0 0 + -130x + x2 = 0 + -3325 -130x + x2 = 0 + -3325 Combine like terms: 0 + -3325 = -3325 -130x + x2 = -3325 The x term is -130x. Take half its coefficient (-65). Square it (4225) and add it to both sides. Add '4225' to each side of the equation. -130x + 4225 + x2 = -3325 + 4225 Reorder the terms: 4225 + -130x + x2 = -3325 + 4225 Combine like terms: -3325 + 4225 = 900 4225 + -130x + x2 = 900 Factor a perfect square on the left side: (x + -65)(x + -65) = 900 Calculate the square root of the right side: 30 Break this problem into two subproblems by setting (x + -65) equal to 30 and -30.Subproblem 1
x + -65 = 30 Simplifying x + -65 = 30 Reorder the terms: -65 + x = 30 Solving -65 + x = 30 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + x = 30 + 65 Combine like terms: -65 + 65 = 0 0 + x = 30 + 65 x = 30 + 65 Combine like terms: 30 + 65 = 95 x = 95 Simplifying x = 95Subproblem 2
x + -65 = -30 Simplifying x + -65 = -30 Reorder the terms: -65 + x = -30 Solving -65 + x = -30 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + x = -30 + 65 Combine like terms: -65 + 65 = 0 0 + x = -30 + 65 x = -30 + 65 Combine like terms: -30 + 65 = 35 x = 35 Simplifying x = 35Solution
The solution to the problem is based on the solutions from the subproblems. x = {95, 35}
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