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Simplifying 4x2 + -12x + -9 = 1 Reorder the terms: -9 + -12x + 4x2 = 1 Solving -9 + -12x + 4x2 = 1 Solving for variable 'x'. Reorder the terms: -9 + -1 + -12x + 4x2 = 1 + -1 Combine like terms: -9 + -1 = -10 -10 + -12x + 4x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -10 + -12x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -6x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -6x + 2x2)' equal to zero and attempt to solve: Simplifying -5 + -6x + 2x2 = 0 Solving -5 + -6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -3x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -3x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -3x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -3x + x2 = 0 + 2.5 -3x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -3x + x2 = 2.5 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 2.5 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 2.5 + 2.25 Combine like terms: 2.5 + 2.25 = 4.75 2.25 + -3x + x2 = 4.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (x + -1.5) equal to 2.179449472 and -2.179449472.Subproblem 1
x + -1.5 = 2.179449472 Simplifying x + -1.5 = 2.179449472 Reorder the terms: -1.5 + x = 2.179449472 Solving -1.5 + x = 2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.179449472 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.179449472 + 1.5 x = 2.179449472 + 1.5 Combine like terms: 2.179449472 + 1.5 = 3.679449472 x = 3.679449472 Simplifying x = 3.679449472Subproblem 2
x + -1.5 = -2.179449472 Simplifying x + -1.5 = -2.179449472 Reorder the terms: -1.5 + x = -2.179449472 Solving -1.5 + x = -2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.179449472 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.179449472 + 1.5 x = -2.179449472 + 1.5 Combine like terms: -2.179449472 + 1.5 = -0.679449472 x = -0.679449472 Simplifying x = -0.679449472Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.679449472, -0.679449472}Solution
x = {3.679449472, -0.679449472}
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