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Simplifying (3x2 + 7x + 4) + -1(5x2 + -4x + 8) = 0 Reorder the terms: (4 + 7x + 3x2) + -1(5x2 + -4x + 8) = 0 Remove parenthesis around (4 + 7x + 3x2) 4 + 7x + 3x2 + -1(5x2 + -4x + 8) = 0 Reorder the terms: 4 + 7x + 3x2 + -1(8 + -4x + 5x2) = 0 4 + 7x + 3x2 + (8 * -1 + -4x * -1 + 5x2 * -1) = 0 4 + 7x + 3x2 + (-8 + 4x + -5x2) = 0 Reorder the terms: 4 + -8 + 7x + 4x + 3x2 + -5x2 = 0 Combine like terms: 4 + -8 = -4 -4 + 7x + 4x + 3x2 + -5x2 = 0 Combine like terms: 7x + 4x = 11x -4 + 11x + 3x2 + -5x2 = 0 Combine like terms: 3x2 + -5x2 = -2x2 -4 + 11x + -2x2 = 0 Solving -4 + 11x + -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'. 2 + -5.5x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -5.5x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -5.5x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5.5x + x2 = 0 + -2 -5.5x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -5.5x + x2 = -2 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = -2 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = -2 + 7.5625 Combine like terms: -2 + 7.5625 = 5.5625 7.5625 + -5.5x + x2 = 5.5625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (x + -2.75) equal to 2.358495283 and -2.358495283.Subproblem 1
x + -2.75 = 2.358495283 Simplifying x + -2.75 = 2.358495283 Reorder the terms: -2.75 + x = 2.358495283 Solving -2.75 + x = 2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 2.358495283 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 2.358495283 + 2.75 x = 2.358495283 + 2.75 Combine like terms: 2.358495283 + 2.75 = 5.108495283 x = 5.108495283 Simplifying x = 5.108495283Subproblem 2
x + -2.75 = -2.358495283 Simplifying x + -2.75 = -2.358495283 Reorder the terms: -2.75 + x = -2.358495283 Solving -2.75 + x = -2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -2.358495283 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -2.358495283 + 2.75 x = -2.358495283 + 2.75 Combine like terms: -2.358495283 + 2.75 = 0.391504717 x = 0.391504717 Simplifying x = 0.391504717Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.108495283, 0.391504717}
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