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Simplifying [2x + -1(4x2 + -7x)] + -1[3x + -1(2x2 + 5x + -4)] = 0 Reorder the terms: [2x + -1(-7x + 4x2)] + -1[3x + -1(2x2 + 5x + -4)] = 0 [2x + (-7x * -1 + 4x2 * -1)] + -1[3x + -1(2x2 + 5x + -4)] = 0 [2x + (7x + -4x2)] + -1[3x + -1(2x2 + 5x + -4)] = 0 Combine like terms: 2x + 7x = 9x [9x + -4x2] + -1[3x + -1(2x2 + 5x + -4)] = 0 Remove brackets around [9x + -4x2] 9x + -4x2 + -1[3x + -1(2x2 + 5x + -4)] = 0 Reorder the terms: 9x + -4x2 + -1[3x + -1(-4 + 5x + 2x2)] = 0 9x + -4x2 + -1[3x + (-4 * -1 + 5x * -1 + 2x2 * -1)] = 0 9x + -4x2 + -1[3x + (4 + -5x + -2x2)] = 0 Reorder the terms: 9x + -4x2 + -1[4 + 3x + -5x + -2x2] = 0 Combine like terms: 3x + -5x = -2x 9x + -4x2 + -1[4 + -2x + -2x2] = 0 9x + -4x2 + [4 * -1 + -2x * -1 + -2x2 * -1] = 0 9x + -4x2 + [-4 + 2x + 2x2] = 0 Reorder the terms: -4 + 9x + 2x + -4x2 + 2x2 = 0 Combine like terms: 9x + 2x = 11x -4 + 11x + -4x2 + 2x2 = 0 Combine like terms: -4x2 + 2x2 = -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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