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Simplifying 7x2 + -64x + -64 = 0 Reorder the terms: -64 + -64x + 7x2 = 0 Solving -64 + -64x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -9.142857143 + -9.142857143x + x2 = 0 Move the constant term to the right: Add '9.142857143' to each side of the equation. -9.142857143 + -9.142857143x + 9.142857143 + x2 = 0 + 9.142857143 Reorder the terms: -9.142857143 + 9.142857143 + -9.142857143x + x2 = 0 + 9.142857143 Combine like terms: -9.142857143 + 9.142857143 = 0.000000000 0.000000000 + -9.142857143x + x2 = 0 + 9.142857143 -9.142857143x + x2 = 0 + 9.142857143 Combine like terms: 0 + 9.142857143 = 9.142857143 -9.142857143x + x2 = 9.142857143 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 = 9.142857143 + 20.89795919 Reorder the terms: 20.89795919 + -9.142857143x + x2 = 9.142857143 + 20.89795919 Combine like terms: 9.142857143 + 20.89795919 = 30.040816333 20.89795919 + -9.142857143x + x2 = 30.040816333 Factor a perfect square on the left side: (x + -4.571428572)(x + -4.571428572) = 30.040816333 Calculate the square root of the right side: 5.480950313 Break this problem into two subproblems by setting (x + -4.571428572) equal to 5.480950313 and -5.480950313.Subproblem 1
x + -4.571428572 = 5.480950313 Simplifying x + -4.571428572 = 5.480950313 Reorder the terms: -4.571428572 + x = 5.480950313 Solving -4.571428572 + x = 5.480950313 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 = 5.480950313 + 4.571428572 Combine like terms: -4.571428572 + 4.571428572 = 0.000000000 0.000000000 + x = 5.480950313 + 4.571428572 x = 5.480950313 + 4.571428572 Combine like terms: 5.480950313 + 4.571428572 = 10.052378885 x = 10.052378885 Simplifying x = 10.052378885Subproblem 2
x + -4.571428572 = -5.480950313 Simplifying x + -4.571428572 = -5.480950313 Reorder the terms: -4.571428572 + x = -5.480950313 Solving -4.571428572 + x = -5.480950313 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 = -5.480950313 + 4.571428572 Combine like terms: -4.571428572 + 4.571428572 = 0.000000000 0.000000000 + x = -5.480950313 + 4.571428572 x = -5.480950313 + 4.571428572 Combine like terms: -5.480950313 + 4.571428572 = -0.909521741 x = -0.909521741 Simplifying x = -0.909521741Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.052378885, -0.909521741}
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