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Simplifying (8x2 + 6x + -5) + -1(10x2 + -9x + 5) = 0 Reorder the terms: (-5 + 6x + 8x2) + -1(10x2 + -9x + 5) = 0 Remove parenthesis around (-5 + 6x + 8x2) -5 + 6x + 8x2 + -1(10x2 + -9x + 5) = 0 Reorder the terms: -5 + 6x + 8x2 + -1(5 + -9x + 10x2) = 0 -5 + 6x + 8x2 + (5 * -1 + -9x * -1 + 10x2 * -1) = 0 -5 + 6x + 8x2 + (-5 + 9x + -10x2) = 0 Reorder the terms: -5 + -5 + 6x + 9x + 8x2 + -10x2 = 0 Combine like terms: -5 + -5 = -10 -10 + 6x + 9x + 8x2 + -10x2 = 0 Combine like terms: 6x + 9x = 15x -10 + 15x + 8x2 + -10x2 = 0 Combine like terms: 8x2 + -10x2 = -2x2 -10 + 15x + -2x2 = 0 Solving -10 + 15x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 5 + -7.5x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -7.5x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -7.5x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7.5x + x2 = 0 + -5 -7.5x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -7.5x + x2 = -5 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = -5 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = -5 + 14.0625 Combine like terms: -5 + 14.0625 = 9.0625 14.0625 + -7.5x + x2 = 9.0625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x + -3.75) equal to 3.010398645 and -3.010398645.Subproblem 1
x + -3.75 = 3.010398645 Simplifying x + -3.75 = 3.010398645 Reorder the terms: -3.75 + x = 3.010398645 Solving -3.75 + x = 3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 3.010398645 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 3.010398645 + 3.75 x = 3.010398645 + 3.75 Combine like terms: 3.010398645 + 3.75 = 6.760398645 x = 6.760398645 Simplifying x = 6.760398645Subproblem 2
x + -3.75 = -3.010398645 Simplifying x + -3.75 = -3.010398645 Reorder the terms: -3.75 + x = -3.010398645 Solving -3.75 + x = -3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -3.010398645 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -3.010398645 + 3.75 x = -3.010398645 + 3.75 Combine like terms: -3.010398645 + 3.75 = 0.739601355 x = 0.739601355 Simplifying x = 0.739601355Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.760398645, 0.739601355}
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