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Simplifying [(2x2 + -4x + 8) + -1(5x2 + 8x + -7)] + -1[(7x2 + 9x + -4) + (-5x2 + 9x + 1)] = 0 Reorder the terms: [(8 + -4x + 2x2) + -1(5x2 + 8x + -7)] + -1[(7x2 + 9x + -4) + (-5x2 + 9x + 1)] = 0 Remove parenthesis around (8 + -4x + 2x2) [8 + -4x + 2x2 + -1(5x2 + 8x + -7)] + -1[(7x2 + 9x + -4) + (-5x2 + 9x + 1)] = 0 Reorder the terms: [8 + -4x + 2x2 + -1(-7 + 8x + 5x2)] + -1[(7x2 + 9x + -4) + (-5x2 + 9x + 1)] = 0 [8 + -4x + 2x2 + (-7 * -1 + 8x * -1 + 5x2 * -1)] + -1[(7x2 + 9x + -4) + (-5x2 + 9x + 1)] = 0 [8 + -4x + 2x2 + (7 + -8x + -5x2)] + -1[(7x2 + 9x + -4) + (-5x2 + 9x + 1)] = 0 Reorder the terms: [8 + 7 + -4x + -8x + 2x2 + -5x2] + -1[(7x2 + 9x + -4) + (-5x2 + 9x + 1)] = 0 Combine like terms: 8 + 7 = 15 [15 + -4x + -8x + 2x2 + -5x2] + -1[(7x2 + 9x + -4) + (-5x2 + 9x + 1)] = 0 Combine like terms: -4x + -8x = -12x [15 + -12x + 2x2 + -5x2] + -1[(7x2 + 9x + -4) + (-5x2 + 9x + 1)] = 0 Combine like terms: 2x2 + -5x2 = -3x2 [15 + -12x + -3x2] + -1[(7x2 + 9x + -4) + (-5x2 + 9x + 1)] = 0 Remove brackets around [15 + -12x + -3x2] 15 + -12x + -3x2 + -1[(7x2 + 9x + -4) + (-5x2 + 9x + 1)] = 0 Reorder the terms: 15 + -12x + -3x2 + -1[(-4 + 9x + 7x2) + (-5x2 + 9x + 1)] = 0 Remove parenthesis around (-4 + 9x + 7x2) 15 + -12x + -3x2 + -1[-4 + 9x + 7x2 + (-5x2 + 9x + 1)] = 0 Reorder the terms: 15 + -12x + -3x2 + -1[-4 + 9x + 7x2 + (1 + 9x + -5x2)] = 0 Remove parenthesis around (1 + 9x + -5x2) 15 + -12x + -3x2 + -1[-4 + 9x + 7x2 + 1 + 9x + -5x2] = 0 Reorder the terms: 15 + -12x + -3x2 + -1[-4 + 1 + 9x + 9x + 7x2 + -5x2] = 0 Combine like terms: -4 + 1 = -3 15 + -12x + -3x2 + -1[-3 + 9x + 9x + 7x2 + -5x2] = 0 Combine like terms: 9x + 9x = 18x 15 + -12x + -3x2 + -1[-3 + 18x + 7x2 + -5x2] = 0 Combine like terms: 7x2 + -5x2 = 2x2 15 + -12x + -3x2 + -1[-3 + 18x + 2x2] = 0 15 + -12x + -3x2 + [-3 * -1 + 18x * -1 + 2x2 * -1] = 0 15 + -12x + -3x2 + [3 + -18x + -2x2] = 0 Reorder the terms: 15 + 3 + -12x + -18x + -3x2 + -2x2 = 0 Combine like terms: 15 + 3 = 18 18 + -12x + -18x + -3x2 + -2x2 = 0 Combine like terms: -12x + -18x = -30x 18 + -30x + -3x2 + -2x2 = 0 Combine like terms: -3x2 + -2x2 = -5x2 18 + -30x + -5x2 = 0 Solving 18 + -30x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -3.6 + 6x + x2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + 6x + 3.6 + x2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + 6x + x2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + 6x + x2 = 0 + 3.6 6x + x2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 6x + x2 = 3.6 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 3.6 + 9 Reorder the terms: 9 + 6x + x2 = 3.6 + 9 Combine like terms: 3.6 + 9 = 12.6 9 + 6x + x2 = 12.6 Factor a perfect square on the left side: (x + 3)(x + 3) = 12.6 Calculate the square root of the right side: 3.54964787 Break this problem into two subproblems by setting (x + 3) equal to 3.54964787 and -3.54964787.Subproblem 1
x + 3 = 3.54964787 Simplifying x + 3 = 3.54964787 Reorder the terms: 3 + x = 3.54964787 Solving 3 + x = 3.54964787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.54964787 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.54964787 + -3 x = 3.54964787 + -3 Combine like terms: 3.54964787 + -3 = 0.54964787 x = 0.54964787 Simplifying x = 0.54964787Subproblem 2
x + 3 = -3.54964787 Simplifying x + 3 = -3.54964787 Reorder the terms: 3 + x = -3.54964787 Solving 3 + x = -3.54964787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.54964787 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.54964787 + -3 x = -3.54964787 + -3 Combine like terms: -3.54964787 + -3 = -6.54964787 x = -6.54964787 Simplifying x = -6.54964787Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.54964787, -6.54964787}
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