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Simplifying 2x + 4 = 1.7x2 + -7x + -230 Reorder the terms: 4 + 2x = 1.7x2 + -7x + -230 Reorder the terms: 4 + 2x = -230 + -7x + 1.7x2 Solving 4 + 2x = -230 + -7x + 1.7x2 Solving for variable 'x'. Reorder the terms: 4 + 230 + 2x + 7x + -1.7x2 = -230 + -7x + 1.7x2 + 230 + 7x + -1.7x2 Combine like terms: 4 + 230 = 234 234 + 2x + 7x + -1.7x2 = -230 + -7x + 1.7x2 + 230 + 7x + -1.7x2 Combine like terms: 2x + 7x = 9x 234 + 9x + -1.7x2 = -230 + -7x + 1.7x2 + 230 + 7x + -1.7x2 Reorder the terms: 234 + 9x + -1.7x2 = -230 + 230 + -7x + 7x + 1.7x2 + -1.7x2 Combine like terms: -230 + 230 = 0 234 + 9x + -1.7x2 = 0 + -7x + 7x + 1.7x2 + -1.7x2 234 + 9x + -1.7x2 = -7x + 7x + 1.7x2 + -1.7x2 Combine like terms: -7x + 7x = 0 234 + 9x + -1.7x2 = 0 + 1.7x2 + -1.7x2 234 + 9x + -1.7x2 = 1.7x2 + -1.7x2 Combine like terms: 1.7x2 + -1.7x2 = 0.0 234 + 9x + -1.7x2 = 0.0 Begin completing the square. Divide all terms by -1.7 the coefficient of the squared term: Divide each side by '-1.7'. -137.6470588 + -5.294117647x + x2 = 0 Move the constant term to the right: Add '137.6470588' to each side of the equation. -137.6470588 + -5.294117647x + 137.6470588 + x2 = 0 + 137.6470588 Reorder the terms: -137.6470588 + 137.6470588 + -5.294117647x + x2 = 0 + 137.6470588 Combine like terms: -137.6470588 + 137.6470588 = 0.0000000 0.0000000 + -5.294117647x + x2 = 0 + 137.6470588 -5.294117647x + x2 = 0 + 137.6470588 Combine like terms: 0 + 137.6470588 = 137.6470588 -5.294117647x + x2 = 137.6470588 The x term is -5.294117647x. Take half its coefficient (-2.647058824). Square it (7.006920418) and add it to both sides. Add '7.006920418' to each side of the equation. -5.294117647x + 7.006920418 + x2 = 137.6470588 + 7.006920418 Reorder the terms: 7.006920418 + -5.294117647x + x2 = 137.6470588 + 7.006920418 Combine like terms: 137.6470588 + 7.006920418 = 144.653979218 7.006920418 + -5.294117647x + x2 = 144.653979218 Factor a perfect square on the left side: (x + -2.647058824)(x + -2.647058824) = 144.653979218 Calculate the square root of the right side: 12.027218266 Break this problem into two subproblems by setting (x + -2.647058824) equal to 12.027218266 and -12.027218266.Subproblem 1
x + -2.647058824 = 12.027218266 Simplifying x + -2.647058824 = 12.027218266 Reorder the terms: -2.647058824 + x = 12.027218266 Solving -2.647058824 + x = 12.027218266 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.647058824' to each side of the equation. -2.647058824 + 2.647058824 + x = 12.027218266 + 2.647058824 Combine like terms: -2.647058824 + 2.647058824 = 0.000000000 0.000000000 + x = 12.027218266 + 2.647058824 x = 12.027218266 + 2.647058824 Combine like terms: 12.027218266 + 2.647058824 = 14.67427709 x = 14.67427709 Simplifying x = 14.67427709Subproblem 2
x + -2.647058824 = -12.027218266 Simplifying x + -2.647058824 = -12.027218266 Reorder the terms: -2.647058824 + x = -12.027218266 Solving -2.647058824 + x = -12.027218266 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.647058824' to each side of the equation. -2.647058824 + 2.647058824 + x = -12.027218266 + 2.647058824 Combine like terms: -2.647058824 + 2.647058824 = 0.000000000 0.000000000 + x = -12.027218266 + 2.647058824 x = -12.027218266 + 2.647058824 Combine like terms: -12.027218266 + 2.647058824 = -9.380159442 x = -9.380159442 Simplifying x = -9.380159442Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.67427709, -9.380159442}
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