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Simplifying 6x2 + 3 + -8x + -5x2 + -13x = 0 Reorder the terms: 3 + -8x + -13x + 6x2 + -5x2 = 0 Combine like terms: -8x + -13x = -21x 3 + -21x + 6x2 + -5x2 = 0 Combine like terms: 6x2 + -5x2 = 1x2 3 + -21x + 1x2 = 0 Solving 3 + -21x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -21x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -21x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -21x + x2 = 0 + -3 -21x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -21x + x2 = -3 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = -3 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -3 + 110.25 Combine like terms: -3 + 110.25 = 107.25 110.25 + -21x + x2 = 107.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 107.25 Calculate the square root of the right side: 10.356157589 Break this problem into two subproblems by setting (x + -10.5) equal to 10.356157589 and -10.356157589.Subproblem 1
x + -10.5 = 10.356157589 Simplifying x + -10.5 = 10.356157589 Reorder the terms: -10.5 + x = 10.356157589 Solving -10.5 + x = 10.356157589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 10.356157589 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 10.356157589 + 10.5 x = 10.356157589 + 10.5 Combine like terms: 10.356157589 + 10.5 = 20.856157589 x = 20.856157589 Simplifying x = 20.856157589Subproblem 2
x + -10.5 = -10.356157589 Simplifying x + -10.5 = -10.356157589 Reorder the terms: -10.5 + x = -10.356157589 Solving -10.5 + x = -10.356157589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -10.356157589 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -10.356157589 + 10.5 x = -10.356157589 + 10.5 Combine like terms: -10.356157589 + 10.5 = 0.143842411 x = 0.143842411 Simplifying x = 0.143842411Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.856157589, 0.143842411}
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