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Simplifying 3x2 + -15x + -6x + -32 = 3 Reorder the terms: -32 + -15x + -6x + 3x2 = 3 Combine like terms: -15x + -6x = -21x -32 + -21x + 3x2 = 3 Solving -32 + -21x + 3x2 = 3 Solving for variable 'x'. Reorder the terms: -32 + -3 + -21x + 3x2 = 3 + -3 Combine like terms: -32 + -3 = -35 -35 + -21x + 3x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -35 + -21x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -11.66666667 + -7x + x2 = 0 Move the constant term to the right: Add '11.66666667' to each side of the equation. -11.66666667 + -7x + 11.66666667 + x2 = 0 + 11.66666667 Reorder the terms: -11.66666667 + 11.66666667 + -7x + x2 = 0 + 11.66666667 Combine like terms: -11.66666667 + 11.66666667 = 0.00000000 0.00000000 + -7x + x2 = 0 + 11.66666667 -7x + x2 = 0 + 11.66666667 Combine like terms: 0 + 11.66666667 = 11.66666667 -7x + x2 = 11.66666667 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 11.66666667 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 11.66666667 + 12.25 Combine like terms: 11.66666667 + 12.25 = 23.91666667 12.25 + -7x + x2 = 23.91666667 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 23.91666667 Calculate the square root of the right side: 4.890466917 Break this problem into two subproblems by setting (x + -3.5) equal to 4.890466917 and -4.890466917.Subproblem 1
x + -3.5 = 4.890466917 Simplifying x + -3.5 = 4.890466917 Reorder the terms: -3.5 + x = 4.890466917 Solving -3.5 + x = 4.890466917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 4.890466917 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.890466917 + 3.5 x = 4.890466917 + 3.5 Combine like terms: 4.890466917 + 3.5 = 8.390466917 x = 8.390466917 Simplifying x = 8.390466917Subproblem 2
x + -3.5 = -4.890466917 Simplifying x + -3.5 = -4.890466917 Reorder the terms: -3.5 + x = -4.890466917 Solving -3.5 + x = -4.890466917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -4.890466917 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.890466917 + 3.5 x = -4.890466917 + 3.5 Combine like terms: -4.890466917 + 3.5 = -1.390466917 x = -1.390466917 Simplifying x = -1.390466917Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.390466917, -1.390466917}
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