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Simplifying 7x2 + -64x + -48 = 0 Reorder the terms: -48 + -64x + 7x2 = 0 Solving -48 + -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'. -6.857142857 + -9.142857143x + x2 = 0 Move the constant term to the right: Add '6.857142857' to each side of the equation. -6.857142857 + -9.142857143x + 6.857142857 + x2 = 0 + 6.857142857 Reorder the terms: -6.857142857 + 6.857142857 + -9.142857143x + x2 = 0 + 6.857142857 Combine like terms: -6.857142857 + 6.857142857 = 0.000000000 0.000000000 + -9.142857143x + x2 = 0 + 6.857142857 -9.142857143x + x2 = 0 + 6.857142857 Combine like terms: 0 + 6.857142857 = 6.857142857 -9.142857143x + x2 = 6.857142857 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 = 6.857142857 + 20.89795919 Reorder the terms: 20.89795919 + -9.142857143x + x2 = 6.857142857 + 20.89795919 Combine like terms: 6.857142857 + 20.89795919 = 27.755102047 20.89795919 + -9.142857143x + x2 = 27.755102047 Factor a perfect square on the left side: (x + -4.571428572)(x + -4.571428572) = 27.755102047 Calculate the square root of the right side: 5.268311119 Break this problem into two subproblems by setting (x + -4.571428572) equal to 5.268311119 and -5.268311119.Subproblem 1
x + -4.571428572 = 5.268311119 Simplifying x + -4.571428572 = 5.268311119 Reorder the terms: -4.571428572 + x = 5.268311119 Solving -4.571428572 + x = 5.268311119 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 = 5.268311119 + 4.571428572 Combine like terms: -4.571428572 + 4.571428572 = 0.000000000 0.000000000 + x = 5.268311119 + 4.571428572 x = 5.268311119 + 4.571428572 Combine like terms: 5.268311119 + 4.571428572 = 9.839739691 x = 9.839739691 Simplifying x = 9.839739691Subproblem 2
x + -4.571428572 = -5.268311119 Simplifying x + -4.571428572 = -5.268311119 Reorder the terms: -4.571428572 + x = -5.268311119 Solving -4.571428572 + x = -5.268311119 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 = -5.268311119 + 4.571428572 Combine like terms: -4.571428572 + 4.571428572 = 0.000000000 0.000000000 + x = -5.268311119 + 4.571428572 x = -5.268311119 + 4.571428572 Combine like terms: -5.268311119 + 4.571428572 = -0.696882547 x = -0.696882547 Simplifying x = -0.696882547Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.839739691, -0.696882547}
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