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Simplifying (0.33) * x2 + (0.5) * x + -12 = -7 Reorder the terms: -12 + 0.5x + 0.33x2 = -7 Solving -12 + 0.5x + 0.33x2 = -7 Solving for variable 'x'. Reorder the terms: -12 + 7 + 0.5x + 0.33x2 = -7 + 7 Combine like terms: -12 + 7 = -5 -5 + 0.5x + 0.33x2 = -7 + 7 Combine like terms: -7 + 7 = 0 -5 + 0.5x + 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'. -15.15151515 + 1.515151515x + x2 = 0 Move the constant term to the right: Add '15.15151515' to each side of the equation. -15.15151515 + 1.515151515x + 15.15151515 + x2 = 0 + 15.15151515 Reorder the terms: -15.15151515 + 15.15151515 + 1.515151515x + x2 = 0 + 15.15151515 Combine like terms: -15.15151515 + 15.15151515 = 0.00000000 0.00000000 + 1.515151515x + x2 = 0 + 15.15151515 1.515151515x + x2 = 0 + 15.15151515 Combine like terms: 0 + 15.15151515 = 15.15151515 1.515151515x + x2 = 15.15151515 The x term is 1.515151515x. Take half its coefficient (0.7575757575). Square it (0.5739210284) and add it to both sides. Add '0.5739210284' to each side of the equation. 1.515151515x + 0.5739210284 + x2 = 15.15151515 + 0.5739210284 Reorder the terms: 0.5739210284 + 1.515151515x + x2 = 15.15151515 + 0.5739210284 Combine like terms: 15.15151515 + 0.5739210284 = 15.7254361784 0.5739210284 + 1.515151515x + x2 = 15.7254361784 Factor a perfect square on the left side: (x + 0.7575757575)(x + 0.7575757575) = 15.7254361784 Calculate the square root of the right side: 3.965531008 Break this problem into two subproblems by setting (x + 0.7575757575) equal to 3.965531008 and -3.965531008.Subproblem 1
x + 0.7575757575 = 3.965531008 Simplifying x + 0.7575757575 = 3.965531008 Reorder the terms: 0.7575757575 + x = 3.965531008 Solving 0.7575757575 + x = 3.965531008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7575757575' to each side of the equation. 0.7575757575 + -0.7575757575 + x = 3.965531008 + -0.7575757575 Combine like terms: 0.7575757575 + -0.7575757575 = 0.0000000000 0.0000000000 + x = 3.965531008 + -0.7575757575 x = 3.965531008 + -0.7575757575 Combine like terms: 3.965531008 + -0.7575757575 = 3.2079552505 x = 3.2079552505 Simplifying x = 3.2079552505Subproblem 2
x + 0.7575757575 = -3.965531008 Simplifying x + 0.7575757575 = -3.965531008 Reorder the terms: 0.7575757575 + x = -3.965531008 Solving 0.7575757575 + x = -3.965531008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7575757575' to each side of the equation. 0.7575757575 + -0.7575757575 + x = -3.965531008 + -0.7575757575 Combine like terms: 0.7575757575 + -0.7575757575 = 0.0000000000 0.0000000000 + x = -3.965531008 + -0.7575757575 x = -3.965531008 + -0.7575757575 Combine like terms: -3.965531008 + -0.7575757575 = -4.7231067655 x = -4.7231067655 Simplifying x = -4.7231067655Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2079552505, -4.7231067655}
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