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Simplifying (8x2 + -4x + 2) + -1(7x2 + 5x + -3) = 0 Reorder the terms: (2 + -4x + 8x2) + -1(7x2 + 5x + -3) = 0 Remove parenthesis around (2 + -4x + 8x2) 2 + -4x + 8x2 + -1(7x2 + 5x + -3) = 0 Reorder the terms: 2 + -4x + 8x2 + -1(-3 + 5x + 7x2) = 0 2 + -4x + 8x2 + (-3 * -1 + 5x * -1 + 7x2 * -1) = 0 2 + -4x + 8x2 + (3 + -5x + -7x2) = 0 Reorder the terms: 2 + 3 + -4x + -5x + 8x2 + -7x2 = 0 Combine like terms: 2 + 3 = 5 5 + -4x + -5x + 8x2 + -7x2 = 0 Combine like terms: -4x + -5x = -9x 5 + -9x + 8x2 + -7x2 = 0 Combine like terms: 8x2 + -7x2 = 1x2 5 + -9x + 1x2 = 0 Solving 5 + -9x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -9x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -9x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -9x + x2 = 0 + -5 -9x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -9x + x2 = -5 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -5 + 20.25 Combine like terms: -5 + 20.25 = 15.25 20.25 + -9x + x2 = 15.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + -4.5) equal to 3.905124838 and -3.905124838.Subproblem 1
x + -4.5 = 3.905124838 Simplifying x + -4.5 = 3.905124838 Reorder the terms: -4.5 + x = 3.905124838 Solving -4.5 + x = 3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 3.905124838 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 3.905124838 + 4.5 x = 3.905124838 + 4.5 Combine like terms: 3.905124838 + 4.5 = 8.405124838 x = 8.405124838 Simplifying x = 8.405124838Subproblem 2
x + -4.5 = -3.905124838 Simplifying x + -4.5 = -3.905124838 Reorder the terms: -4.5 + x = -3.905124838 Solving -4.5 + x = -3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -3.905124838 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -3.905124838 + 4.5 x = -3.905124838 + 4.5 Combine like terms: -3.905124838 + 4.5 = 0.594875162 x = 0.594875162 Simplifying x = 0.594875162Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.405124838, 0.594875162}
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