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Simplifying 4x2 + -30x + 9 = 12x2 + -11x + -28 Reorder the terms: 9 + -30x + 4x2 = 12x2 + -11x + -28 Reorder the terms: 9 + -30x + 4x2 = -28 + -11x + 12x2 Solving 9 + -30x + 4x2 = -28 + -11x + 12x2 Solving for variable 'x'. Reorder the terms: 9 + 28 + -30x + 11x + 4x2 + -12x2 = -28 + -11x + 12x2 + 28 + 11x + -12x2 Combine like terms: 9 + 28 = 37 37 + -30x + 11x + 4x2 + -12x2 = -28 + -11x + 12x2 + 28 + 11x + -12x2 Combine like terms: -30x + 11x = -19x 37 + -19x + 4x2 + -12x2 = -28 + -11x + 12x2 + 28 + 11x + -12x2 Combine like terms: 4x2 + -12x2 = -8x2 37 + -19x + -8x2 = -28 + -11x + 12x2 + 28 + 11x + -12x2 Reorder the terms: 37 + -19x + -8x2 = -28 + 28 + -11x + 11x + 12x2 + -12x2 Combine like terms: -28 + 28 = 0 37 + -19x + -8x2 = 0 + -11x + 11x + 12x2 + -12x2 37 + -19x + -8x2 = -11x + 11x + 12x2 + -12x2 Combine like terms: -11x + 11x = 0 37 + -19x + -8x2 = 0 + 12x2 + -12x2 37 + -19x + -8x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 37 + -19x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -4.625 + 2.375x + x2 = 0 Move the constant term to the right: Add '4.625' to each side of the equation. -4.625 + 2.375x + 4.625 + x2 = 0 + 4.625 Reorder the terms: -4.625 + 4.625 + 2.375x + x2 = 0 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + 2.375x + x2 = 0 + 4.625 2.375x + x2 = 0 + 4.625 Combine like terms: 0 + 4.625 = 4.625 2.375x + x2 = 4.625 The x term is 2.375x. Take half its coefficient (1.1875). Square it (1.41015625) and add it to both sides. Add '1.41015625' to each side of the equation. 2.375x + 1.41015625 + x2 = 4.625 + 1.41015625 Reorder the terms: 1.41015625 + 2.375x + x2 = 4.625 + 1.41015625 Combine like terms: 4.625 + 1.41015625 = 6.03515625 1.41015625 + 2.375x + x2 = 6.03515625 Factor a perfect square on the left side: (x + 1.1875)(x + 1.1875) = 6.03515625 Calculate the square root of the right side: 2.456655501 Break this problem into two subproblems by setting (x + 1.1875) equal to 2.456655501 and -2.456655501.Subproblem 1
x + 1.1875 = 2.456655501 Simplifying x + 1.1875 = 2.456655501 Reorder the terms: 1.1875 + x = 2.456655501 Solving 1.1875 + x = 2.456655501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + x = 2.456655501 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + x = 2.456655501 + -1.1875 x = 2.456655501 + -1.1875 Combine like terms: 2.456655501 + -1.1875 = 1.269155501 x = 1.269155501 Simplifying x = 1.269155501Subproblem 2
x + 1.1875 = -2.456655501 Simplifying x + 1.1875 = -2.456655501 Reorder the terms: 1.1875 + x = -2.456655501 Solving 1.1875 + x = -2.456655501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + x = -2.456655501 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + x = -2.456655501 + -1.1875 x = -2.456655501 + -1.1875 Combine like terms: -2.456655501 + -1.1875 = -3.644155501 x = -3.644155501 Simplifying x = -3.644155501Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.269155501, -3.644155501}
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