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Simplifying 0.5x2 + 3x + -1 = 19 Reorder the terms: -1 + 3x + 0.5x2 = 19 Solving -1 + 3x + 0.5x2 = 19 Solving for variable 'x'. Reorder the terms: -1 + -19 + 3x + 0.5x2 = 19 + -19 Combine like terms: -1 + -19 = -20 -20 + 3x + 0.5x2 = 19 + -19 Combine like terms: 19 + -19 = 0 -20 + 3x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -40 + 6x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 6x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 6x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 6x + x2 = 0 + 40 6x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 6x + x2 = 40 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 40 + 9 Reorder the terms: 9 + 6x + x2 = 40 + 9 Combine like terms: 40 + 9 = 49 9 + 6x + x2 = 49 Factor a perfect square on the left side: (x + 3)(x + 3) = 49 Calculate the square root of the right side: 7 Break this problem into two subproblems by setting (x + 3) equal to 7 and -7.Subproblem 1
x + 3 = 7 Simplifying x + 3 = 7 Reorder the terms: 3 + x = 7 Solving 3 + x = 7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 7 + -3 Combine like terms: 3 + -3 = 0 0 + x = 7 + -3 x = 7 + -3 Combine like terms: 7 + -3 = 4 x = 4 Simplifying x = 4Subproblem 2
x + 3 = -7 Simplifying x + 3 = -7 Reorder the terms: 3 + x = -7 Solving 3 + x = -7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -7 + -3 Combine like terms: 3 + -3 = 0 0 + x = -7 + -3 x = -7 + -3 Combine like terms: -7 + -3 = -10 x = -10 Simplifying x = -10Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, -10}
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