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Simplifying -0.02x2 + 0.92x + 4 = 0.2x + 7.6 Reorder the terms: 4 + 0.92x + -0.02x2 = 0.2x + 7.6 Reorder the terms: 4 + 0.92x + -0.02x2 = 7.6 + 0.2x Solving 4 + 0.92x + -0.02x2 = 7.6 + 0.2x Solving for variable 'x'. Reorder the terms: 4 + -7.6 + 0.92x + -0.2x + -0.02x2 = 7.6 + 0.2x + -7.6 + -0.2x Combine like terms: 4 + -7.6 = -3.6 -3.6 + 0.92x + -0.2x + -0.02x2 = 7.6 + 0.2x + -7.6 + -0.2x Combine like terms: 0.92x + -0.2x = 0.72x -3.6 + 0.72x + -0.02x2 = 7.6 + 0.2x + -7.6 + -0.2x Reorder the terms: -3.6 + 0.72x + -0.02x2 = 7.6 + -7.6 + 0.2x + -0.2x Combine like terms: 7.6 + -7.6 = 0.0 -3.6 + 0.72x + -0.02x2 = 0.0 + 0.2x + -0.2x -3.6 + 0.72x + -0.02x2 = 0.2x + -0.2x Combine like terms: 0.2x + -0.2x = 0.0 -3.6 + 0.72x + -0.02x2 = 0.0 Begin completing the square. Divide all terms by -0.02 the coefficient of the squared term: Divide each side by '-0.02'. 180 + -36x + x2 = 0 Move the constant term to the right: Add '-180' to each side of the equation. 180 + -36x + -180 + x2 = 0 + -180 Reorder the terms: 180 + -180 + -36x + x2 = 0 + -180 Combine like terms: 180 + -180 = 0 0 + -36x + x2 = 0 + -180 -36x + x2 = 0 + -180 Combine like terms: 0 + -180 = -180 -36x + x2 = -180 The x term is -36x. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36x + 324 + x2 = -180 + 324 Reorder the terms: 324 + -36x + x2 = -180 + 324 Combine like terms: -180 + 324 = 144 324 + -36x + x2 = 144 Factor a perfect square on the left side: (x + -18)(x + -18) = 144 Calculate the square root of the right side: 12 Break this problem into two subproblems by setting (x + -18) equal to 12 and -12.Subproblem 1
x + -18 = 12 Simplifying x + -18 = 12 Reorder the terms: -18 + x = 12 Solving -18 + x = 12 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 12 + 18 Combine like terms: -18 + 18 = 0 0 + x = 12 + 18 x = 12 + 18 Combine like terms: 12 + 18 = 30 x = 30 Simplifying x = 30Subproblem 2
x + -18 = -12 Simplifying x + -18 = -12 Reorder the terms: -18 + x = -12 Solving -18 + x = -12 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = -12 + 18 Combine like terms: -18 + 18 = 0 0 + x = -12 + 18 x = -12 + 18 Combine like terms: -12 + 18 = 6 x = 6 Simplifying x = 6Solution
The solution to the problem is based on the solutions from the subproblems. x = {30, 6}
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