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Simplifying 7x2 + -64x + -9 = 0 Reorder the terms: -9 + -64x + 7x2 = 0 Solving -9 + -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'. -1.285714286 + -9.142857143x + x2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + -9.142857143x + 1.285714286 + x2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + -9.142857143x + x2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + -9.142857143x + x2 = 0 + 1.285714286 -9.142857143x + x2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 -9.142857143x + x2 = 1.285714286 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 = 1.285714286 + 20.89795919 Reorder the terms: 20.89795919 + -9.142857143x + x2 = 1.285714286 + 20.89795919 Combine like terms: 1.285714286 + 20.89795919 = 22.183673476 20.89795919 + -9.142857143x + x2 = 22.183673476 Factor a perfect square on the left side: (x + -4.571428572)(x + -4.571428572) = 22.183673476 Calculate the square root of the right side: 4.709954721 Break this problem into two subproblems by setting (x + -4.571428572) equal to 4.709954721 and -4.709954721.Subproblem 1
x + -4.571428572 = 4.709954721 Simplifying x + -4.571428572 = 4.709954721 Reorder the terms: -4.571428572 + x = 4.709954721 Solving -4.571428572 + x = 4.709954721 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 = 4.709954721 + 4.571428572 Combine like terms: -4.571428572 + 4.571428572 = 0.000000000 0.000000000 + x = 4.709954721 + 4.571428572 x = 4.709954721 + 4.571428572 Combine like terms: 4.709954721 + 4.571428572 = 9.281383293 x = 9.281383293 Simplifying x = 9.281383293Subproblem 2
x + -4.571428572 = -4.709954721 Simplifying x + -4.571428572 = -4.709954721 Reorder the terms: -4.571428572 + x = -4.709954721 Solving -4.571428572 + x = -4.709954721 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 = -4.709954721 + 4.571428572 Combine like terms: -4.571428572 + 4.571428572 = 0.000000000 0.000000000 + x = -4.709954721 + 4.571428572 x = -4.709954721 + 4.571428572 Combine like terms: -4.709954721 + 4.571428572 = -0.138526149 x = -0.138526149 Simplifying x = -0.138526149Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.281383293, -0.138526149}
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