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Simplifying 0.33(x + 2)(x + 2) + -5 = 22 Reorder the terms: 0.33(2 + x)(x + 2) + -5 = 22 Reorder the terms: 0.33(2 + x)(2 + x) + -5 = 22 Multiply (2 + x) * (2 + x) 0.33(2(2 + x) + x(2 + x)) + -5 = 22 0.33((2 * 2 + x * 2) + x(2 + x)) + -5 = 22 0.33((4 + 2x) + x(2 + x)) + -5 = 22 0.33(4 + 2x + (2 * x + x * x)) + -5 = 22 0.33(4 + 2x + (2x + x2)) + -5 = 22 Combine like terms: 2x + 2x = 4x 0.33(4 + 4x + x2) + -5 = 22 (4 * 0.33 + 4x * 0.33 + x2 * 0.33) + -5 = 22 (1.32 + 1.32x + 0.33x2) + -5 = 22 Reorder the terms: 1.32 + -5 + 1.32x + 0.33x2 = 22 Combine like terms: 1.32 + -5 = -3.68 -3.68 + 1.32x + 0.33x2 = 22 Solving -3.68 + 1.32x + 0.33x2 = 22 Solving for variable 'x'. Reorder the terms: -3.68 + -22 + 1.32x + 0.33x2 = 22 + -22 Combine like terms: -3.68 + -22 = -25.68 -25.68 + 1.32x + 0.33x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -25.68 + 1.32x + 0.33x2 = 0 Begin completing the square. Divide all terms by 0.33 the coefficient of the squared term: Divide each side by '0.33'. -77.81818182 + 4x + x2 = 0 Move the constant term to the right: Add '77.81818182' to each side of the equation. -77.81818182 + 4x + 77.81818182 + x2 = 0 + 77.81818182 Reorder the terms: -77.81818182 + 77.81818182 + 4x + x2 = 0 + 77.81818182 Combine like terms: -77.81818182 + 77.81818182 = 0.00000000 0.00000000 + 4x + x2 = 0 + 77.81818182 4x + x2 = 0 + 77.81818182 Combine like terms: 0 + 77.81818182 = 77.81818182 4x + x2 = 77.81818182 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 77.81818182 + 4 Reorder the terms: 4 + 4x + x2 = 77.81818182 + 4 Combine like terms: 77.81818182 + 4 = 81.81818182 4 + 4x + x2 = 81.81818182 Factor a perfect square on the left side: (x + 2)(x + 2) = 81.81818182 Calculate the square root of the right side: 9.045340337 Break this problem into two subproblems by setting (x + 2) equal to 9.045340337 and -9.045340337.Subproblem 1
x + 2 = 9.045340337 Simplifying x + 2 = 9.045340337 Reorder the terms: 2 + x = 9.045340337 Solving 2 + x = 9.045340337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 9.045340337 + -2 Combine like terms: 2 + -2 = 0 0 + x = 9.045340337 + -2 x = 9.045340337 + -2 Combine like terms: 9.045340337 + -2 = 7.045340337 x = 7.045340337 Simplifying x = 7.045340337Subproblem 2
x + 2 = -9.045340337 Simplifying x + 2 = -9.045340337 Reorder the terms: 2 + x = -9.045340337 Solving 2 + x = -9.045340337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -9.045340337 + -2 Combine like terms: 2 + -2 = 0 0 + x = -9.045340337 + -2 x = -9.045340337 + -2 Combine like terms: -9.045340337 + -2 = -11.045340337 x = -11.045340337 Simplifying x = -11.045340337Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.045340337, -11.045340337}
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