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Simplifying 5x2 + -21x + 4 + -1x2 + -11x + 6 = 0 Reorder the terms: 4 + 6 + -21x + -11x + 5x2 + -1x2 = 0 Combine like terms: 4 + 6 = 10 10 + -21x + -11x + 5x2 + -1x2 = 0 Combine like terms: -21x + -11x = -32x 10 + -32x + 5x2 + -1x2 = 0 Combine like terms: 5x2 + -1x2 = 4x2 10 + -32x + 4x2 = 0 Solving 10 + -32x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -16x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -16x + 2x2)' equal to zero and attempt to solve: Simplifying 5 + -16x + 2x2 = 0 Solving 5 + -16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -8x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -8x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -8x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -8x + x2 = 0 + -2.5 -8x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -8x + x2 = -2.5 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -2.5 + 16 Reorder the terms: 16 + -8x + x2 = -2.5 + 16 Combine like terms: -2.5 + 16 = 13.5 16 + -8x + x2 = 13.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 13.5 Calculate the square root of the right side: 3.674234614 Break this problem into two subproblems by setting (x + -4) equal to 3.674234614 and -3.674234614.Subproblem 1
x + -4 = 3.674234614 Simplifying x + -4 = 3.674234614 Reorder the terms: -4 + x = 3.674234614 Solving -4 + x = 3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.674234614 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.674234614 + 4 x = 3.674234614 + 4 Combine like terms: 3.674234614 + 4 = 7.674234614 x = 7.674234614 Simplifying x = 7.674234614Subproblem 2
x + -4 = -3.674234614 Simplifying x + -4 = -3.674234614 Reorder the terms: -4 + x = -3.674234614 Solving -4 + x = -3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.674234614 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.674234614 + 4 x = -3.674234614 + 4 Combine like terms: -3.674234614 + 4 = 0.325765386 x = 0.325765386 Simplifying x = 0.325765386Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.674234614, 0.325765386}Solution
x = {7.674234614, 0.325765386}
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