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Simplifying (4x2 + -7x + 3) + -1(2x2 + 9x + -8) = 0 Reorder the terms: (3 + -7x + 4x2) + -1(2x2 + 9x + -8) = 0 Remove parenthesis around (3 + -7x + 4x2) 3 + -7x + 4x2 + -1(2x2 + 9x + -8) = 0 Reorder the terms: 3 + -7x + 4x2 + -1(-8 + 9x + 2x2) = 0 3 + -7x + 4x2 + (-8 * -1 + 9x * -1 + 2x2 * -1) = 0 3 + -7x + 4x2 + (8 + -9x + -2x2) = 0 Reorder the terms: 3 + 8 + -7x + -9x + 4x2 + -2x2 = 0 Combine like terms: 3 + 8 = 11 11 + -7x + -9x + 4x2 + -2x2 = 0 Combine like terms: -7x + -9x = -16x 11 + -16x + 4x2 + -2x2 = 0 Combine like terms: 4x2 + -2x2 = 2x2 11 + -16x + 2x2 = 0 Solving 11 + -16x + 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'. 5.5 + -8x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -8x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -8x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -8x + x2 = 0 + -5.5 -8x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -8x + x2 = -5.5 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 = -5.5 + 16 Reorder the terms: 16 + -8x + x2 = -5.5 + 16 Combine like terms: -5.5 + 16 = 10.5 16 + -8x + x2 = 10.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 10.5 Calculate the square root of the right side: 3.240370349 Break this problem into two subproblems by setting (x + -4) equal to 3.240370349 and -3.240370349.Subproblem 1
x + -4 = 3.240370349 Simplifying x + -4 = 3.240370349 Reorder the terms: -4 + x = 3.240370349 Solving -4 + x = 3.240370349 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 = 3.240370349 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.240370349 + 4 x = 3.240370349 + 4 Combine like terms: 3.240370349 + 4 = 7.240370349 x = 7.240370349 Simplifying x = 7.240370349Subproblem 2
x + -4 = -3.240370349 Simplifying x + -4 = -3.240370349 Reorder the terms: -4 + x = -3.240370349 Solving -4 + x = -3.240370349 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 = -3.240370349 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.240370349 + 4 x = -3.240370349 + 4 Combine like terms: -3.240370349 + 4 = 0.759629651 x = 0.759629651 Simplifying x = 0.759629651Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.240370349, 0.759629651}
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