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Simplifying 0 = -0.375x2 + -0.75x + 30 Reorder the terms: 0 = 30 + -0.75x + -0.375x2 Solving 0 = 30 + -0.75x + -0.375x2 Solving for variable 'x'. Combine like terms: 0 + -30 = -30 -30 + 0.75x + 0.375x2 = 30 + -0.75x + -0.375x2 + -30 + 0.75x + 0.375x2 Reorder the terms: -30 + 0.75x + 0.375x2 = 30 + -30 + -0.75x + 0.75x + -0.375x2 + 0.375x2 Combine like terms: 30 + -30 = 0 -30 + 0.75x + 0.375x2 = 0 + -0.75x + 0.75x + -0.375x2 + 0.375x2 -30 + 0.75x + 0.375x2 = -0.75x + 0.75x + -0.375x2 + 0.375x2 Combine like terms: -0.75x + 0.75x = 0.00 -30 + 0.75x + 0.375x2 = 0.00 + -0.375x2 + 0.375x2 -30 + 0.75x + 0.375x2 = -0.375x2 + 0.375x2 Combine like terms: -0.375x2 + 0.375x2 = 0.000 -30 + 0.75x + 0.375x2 = 0.000 Begin completing the square. Divide all terms by 0.375 the coefficient of the squared term: Divide each side by '0.375'. -80 + 2x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + 2x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 2x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 2x + x2 = 0 + 80 2x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 2x + x2 = 80 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 80 + 1 Reorder the terms: 1 + 2x + x2 = 80 + 1 Combine like terms: 80 + 1 = 81 1 + 2x + x2 = 81 Factor a perfect square on the left side: (x + 1)(x + 1) = 81 Calculate the square root of the right side: 9 Break this problem into two subproblems by setting (x + 1) equal to 9 and -9.Subproblem 1
x + 1 = 9 Simplifying x + 1 = 9 Reorder the terms: 1 + x = 9 Solving 1 + x = 9 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 9 + -1 Combine like terms: 1 + -1 = 0 0 + x = 9 + -1 x = 9 + -1 Combine like terms: 9 + -1 = 8 x = 8 Simplifying x = 8Subproblem 2
x + 1 = -9 Simplifying x + 1 = -9 Reorder the terms: 1 + x = -9 Solving 1 + x = -9 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -9 + -1 Combine like terms: 1 + -1 = 0 0 + x = -9 + -1 x = -9 + -1 Combine like terms: -9 + -1 = -10 x = -10 Simplifying x = -10Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, -10}
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