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Simplifying -11x2 + 8x + -9x2 + 6 = 0 Reorder the terms: 6 + 8x + -11x2 + -9x2 = 0 Combine like terms: -11x2 + -9x2 = -20x2 6 + 8x + -20x2 = 0 Solving 6 + 8x + -20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 4x + -10x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 4x + -10x2)' equal to zero and attempt to solve: Simplifying 3 + 4x + -10x2 = 0 Solving 3 + 4x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.3 + -0.4x + x2 = 0.0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -0.4x + 0.3 + x2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + -0.4x + x2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -0.4x + x2 = 0.0 + 0.3 -0.4x + x2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 -0.4x + x2 = 0.3 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 0.3 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 0.3 + 0.04 Combine like terms: 0.3 + 0.04 = 0.34 0.04 + -0.4x + x2 = 0.34 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.34 Calculate the square root of the right side: 0.583095189 Break this problem into two subproblems by setting (x + -0.2) equal to 0.583095189 and -0.583095189.Subproblem 1
x + -0.2 = 0.583095189 Simplifying x + -0.2 = 0.583095189 Reorder the terms: -0.2 + x = 0.583095189 Solving -0.2 + x = 0.583095189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 0.583095189 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.583095189 + 0.2 x = 0.583095189 + 0.2 Combine like terms: 0.583095189 + 0.2 = 0.783095189 x = 0.783095189 Simplifying x = 0.783095189Subproblem 2
x + -0.2 = -0.583095189 Simplifying x + -0.2 = -0.583095189 Reorder the terms: -0.2 + x = -0.583095189 Solving -0.2 + x = -0.583095189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -0.583095189 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.583095189 + 0.2 x = -0.583095189 + 0.2 Combine like terms: -0.583095189 + 0.2 = -0.383095189 x = -0.383095189 Simplifying x = -0.383095189Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.783095189, -0.383095189}Solution
x = {0.783095189, -0.383095189}
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