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Simplifying 0.25x2 + -1.5x = 10 Reorder the terms: -1.5x + 0.25x2 = 10 Solving -1.5x + 0.25x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + -1.5x + 0.25x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -1.5x + 0.25x2 = 0 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -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 = 10 x = 10 Simplifying x = 10Subproblem 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 = -4 x = -4 Simplifying x = -4Solution
The solution to the problem is based on the solutions from the subproblems. x = {10, -4}
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