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Simplifying -0.25(x + 3)(x + 3) + 5 = 2 Reorder the terms: -0.25(3 + x)(x + 3) + 5 = 2 Reorder the terms: -0.25(3 + x)(3 + x) + 5 = 2 Multiply (3 + x) * (3 + x) -0.25(3(3 + x) + x(3 + x)) + 5 = 2 -0.25((3 * 3 + x * 3) + x(3 + x)) + 5 = 2 -0.25((9 + 3x) + x(3 + x)) + 5 = 2 -0.25(9 + 3x + (3 * x + x * x)) + 5 = 2 -0.25(9 + 3x + (3x + x2)) + 5 = 2 Combine like terms: 3x + 3x = 6x -0.25(9 + 6x + x2) + 5 = 2 (9 * -0.25 + 6x * -0.25 + x2 * -0.25) + 5 = 2 (-2.25 + -1.5x + -0.25x2) + 5 = 2 Reorder the terms: -2.25 + 5 + -1.5x + -0.25x2 = 2 Combine like terms: -2.25 + 5 = 2.75 2.75 + -1.5x + -0.25x2 = 2 Solving 2.75 + -1.5x + -0.25x2 = 2 Solving for variable 'x'. Reorder the terms: 2.75 + -2 + -1.5x + -0.25x2 = 2 + -2 Combine like terms: 2.75 + -2 = 0.75 0.75 + -1.5x + -0.25x2 = 2 + -2 Combine like terms: 2 + -2 = 0 0.75 + -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'. -3 + 6x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 6x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 6x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 6x + x2 = 0 + 3 6x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 6x + x2 = 3 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 = 3 + 9 Reorder the terms: 9 + 6x + x2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + 6x + x2 = 12 Factor a perfect square on the left side: (x + 3)(x + 3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + 3) equal to 3.464101615 and -3.464101615.Subproblem 1
x + 3 = 3.464101615 Simplifying x + 3 = 3.464101615 Reorder the terms: 3 + x = 3.464101615 Solving 3 + x = 3.464101615 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 = 3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.464101615 + -3 x = 3.464101615 + -3 Combine like terms: 3.464101615 + -3 = 0.464101615 x = 0.464101615 Simplifying x = 0.464101615Subproblem 2
x + 3 = -3.464101615 Simplifying x + 3 = -3.464101615 Reorder the terms: 3 + x = -3.464101615 Solving 3 + x = -3.464101615 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 = -3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.464101615 + -3 x = -3.464101615 + -3 Combine like terms: -3.464101615 + -3 = -6.464101615 x = -6.464101615 Simplifying x = -6.464101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.464101615, -6.464101615}
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