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Simplifying -7x2 + -64x + -1 = 0 Reorder the terms: -1 + -64x + -7x2 = 0 Solving -1 + -64x + -7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 64x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 64x + 7x2)' equal to zero and attempt to solve: Simplifying 1 + 64x + 7x2 = 0 Solving 1 + 64x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + 9.142857143x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 9.142857143x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 9.142857143x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 9.142857143x + x2 = 0 + -0.1428571429 9.142857143x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 9.142857143x + x2 = -0.1428571429 The x term is 9.142857143x. Take half its coefficient (4.571428572). Square it (20.89795919) and add it to both sides. Add '20.89795919' to each side of the equation. 9.142857143x + 20.89795919 + x2 = -0.1428571429 + 20.89795919 Reorder the terms: 20.89795919 + 9.142857143x + x2 = -0.1428571429 + 20.89795919 Combine like terms: -0.1428571429 + 20.89795919 = 20.7551020471 20.89795919 + 9.142857143x + x2 = 20.7551020471 Factor a perfect square on the left side: (x + 4.571428572)(x + 4.571428572) = 20.7551020471 Calculate the square root of the right side: 4.555776778 Break this problem into two subproblems by setting (x + 4.571428572) equal to 4.555776778 and -4.555776778.Subproblem 1
x + 4.571428572 = 4.555776778 Simplifying x + 4.571428572 = 4.555776778 Reorder the terms: 4.571428572 + x = 4.555776778 Solving 4.571428572 + x = 4.555776778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.571428572' to each side of the equation. 4.571428572 + -4.571428572 + x = 4.555776778 + -4.571428572 Combine like terms: 4.571428572 + -4.571428572 = 0.000000000 0.000000000 + x = 4.555776778 + -4.571428572 x = 4.555776778 + -4.571428572 Combine like terms: 4.555776778 + -4.571428572 = -0.015651794 x = -0.015651794 Simplifying x = -0.015651794Subproblem 2
x + 4.571428572 = -4.555776778 Simplifying x + 4.571428572 = -4.555776778 Reorder the terms: 4.571428572 + x = -4.555776778 Solving 4.571428572 + x = -4.555776778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.571428572' to each side of the equation. 4.571428572 + -4.571428572 + x = -4.555776778 + -4.571428572 Combine like terms: 4.571428572 + -4.571428572 = 0.000000000 0.000000000 + x = -4.555776778 + -4.571428572 x = -4.555776778 + -4.571428572 Combine like terms: -4.555776778 + -4.571428572 = -9.12720535 x = -9.12720535 Simplifying x = -9.12720535Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.015651794, -9.12720535}Solution
x = {-0.015651794, -9.12720535}
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