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Simplifying 4x2 + -12x + 9 = x2 + -1 Reorder the terms: 9 + -12x + 4x2 = x2 + -1 Reorder the terms: 9 + -12x + 4x2 = -1 + x2 Solving 9 + -12x + 4x2 = -1 + x2 Solving for variable 'x'. Reorder the terms: 9 + 1 + -12x + 4x2 + -1x2 = -1 + x2 + 1 + -1x2 Combine like terms: 9 + 1 = 10 10 + -12x + 4x2 + -1x2 = -1 + x2 + 1 + -1x2 Combine like terms: 4x2 + -1x2 = 3x2 10 + -12x + 3x2 = -1 + x2 + 1 + -1x2 Reorder the terms: 10 + -12x + 3x2 = -1 + 1 + x2 + -1x2 Combine like terms: -1 + 1 = 0 10 + -12x + 3x2 = 0 + x2 + -1x2 10 + -12x + 3x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 10 + -12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.333333333 + -4x + x2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + -4x + -3.333333333 + x2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + -4x + x2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + -4x + x2 = 0 + -3.333333333 -4x + x2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 -4x + x2 = -3.333333333 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 = -3.333333333 + 4 Reorder the terms: 4 + -4x + x2 = -3.333333333 + 4 Combine like terms: -3.333333333 + 4 = 0.666666667 4 + -4x + x2 = 0.666666667 Factor a perfect square on the left side: (x + -2)(x + -2) = 0.666666667 Calculate the square root of the right side: 0.816496581 Break this problem into two subproblems by setting (x + -2) equal to 0.816496581 and -0.816496581.Subproblem 1
x + -2 = 0.816496581 Simplifying x + -2 = 0.816496581 Reorder the terms: -2 + x = 0.816496581 Solving -2 + x = 0.816496581 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 = 0.816496581 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0.816496581 + 2 x = 0.816496581 + 2 Combine like terms: 0.816496581 + 2 = 2.816496581 x = 2.816496581 Simplifying x = 2.816496581Subproblem 2
x + -2 = -0.816496581 Simplifying x + -2 = -0.816496581 Reorder the terms: -2 + x = -0.816496581 Solving -2 + x = -0.816496581 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 = -0.816496581 + 2 Combine like terms: -2 + 2 = 0 0 + x = -0.816496581 + 2 x = -0.816496581 + 2 Combine like terms: -0.816496581 + 2 = 1.183503419 x = 1.183503419 Simplifying x = 1.183503419Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.816496581, 1.183503419}
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