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Simplifying -0.2x2 + 3.6x + 23 = 7 Reorder the terms: 23 + 3.6x + -0.2x2 = 7 Solving 23 + 3.6x + -0.2x2 = 7 Solving for variable 'x'. Reorder the terms: 23 + -7 + 3.6x + -0.2x2 = 7 + -7 Combine like terms: 23 + -7 = 16 16 + 3.6x + -0.2x2 = 7 + -7 Combine like terms: 7 + -7 = 0 16 + 3.6x + -0.2x2 = 0 Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. -80 + -18x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + -18x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + -18x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -18x + x2 = 0 + 80 -18x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 -18x + x2 = 80 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 80 + 81 Reorder the terms: 81 + -18x + x2 = 80 + 81 Combine like terms: 80 + 81 = 161 81 + -18x + x2 = 161 Factor a perfect square on the left side: (x + -9)(x + -9) = 161 Calculate the square root of the right side: 12.68857754 Break this problem into two subproblems by setting (x + -9) equal to 12.68857754 and -12.68857754.Subproblem 1
x + -9 = 12.68857754 Simplifying x + -9 = 12.68857754 Reorder the terms: -9 + x = 12.68857754 Solving -9 + x = 12.68857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 12.68857754 + 9 Combine like terms: -9 + 9 = 0 0 + x = 12.68857754 + 9 x = 12.68857754 + 9 Combine like terms: 12.68857754 + 9 = 21.68857754 x = 21.68857754 Simplifying x = 21.68857754Subproblem 2
x + -9 = -12.68857754 Simplifying x + -9 = -12.68857754 Reorder the terms: -9 + x = -12.68857754 Solving -9 + x = -12.68857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -12.68857754 + 9 Combine like terms: -9 + 9 = 0 0 + x = -12.68857754 + 9 x = -12.68857754 + 9 Combine like terms: -12.68857754 + 9 = -3.68857754 x = -3.68857754 Simplifying x = -3.68857754Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.68857754, -3.68857754}
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