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Simplifying 9x2 + 49x + 64 = 0 Reorder the terms: 64 + 49x + 9x2 = 0 Solving 64 + 49x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 7.111111111 + 5.444444444x + x2 = 0 Move the constant term to the right: Add '-7.111111111' to each side of the equation. 7.111111111 + 5.444444444x + -7.111111111 + x2 = 0 + -7.111111111 Reorder the terms: 7.111111111 + -7.111111111 + 5.444444444x + x2 = 0 + -7.111111111 Combine like terms: 7.111111111 + -7.111111111 = 0.000000000 0.000000000 + 5.444444444x + x2 = 0 + -7.111111111 5.444444444x + x2 = 0 + -7.111111111 Combine like terms: 0 + -7.111111111 = -7.111111111 5.444444444x + x2 = -7.111111111 The x term is 5.444444444x. Take half its coefficient (2.722222222). Square it (7.410493826) and add it to both sides. Add '7.410493826' to each side of the equation. 5.444444444x + 7.410493826 + x2 = -7.111111111 + 7.410493826 Reorder the terms: 7.410493826 + 5.444444444x + x2 = -7.111111111 + 7.410493826 Combine like terms: -7.111111111 + 7.410493826 = 0.299382715 7.410493826 + 5.444444444x + x2 = 0.299382715 Factor a perfect square on the left side: (x + 2.722222222)(x + 2.722222222) = 0.299382715 Calculate the square root of the right side: 0.547158766 Break this problem into two subproblems by setting (x + 2.722222222) equal to 0.547158766 and -0.547158766.Subproblem 1
x + 2.722222222 = 0.547158766 Simplifying x + 2.722222222 = 0.547158766 Reorder the terms: 2.722222222 + x = 0.547158766 Solving 2.722222222 + x = 0.547158766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.722222222' to each side of the equation. 2.722222222 + -2.722222222 + x = 0.547158766 + -2.722222222 Combine like terms: 2.722222222 + -2.722222222 = 0.000000000 0.000000000 + x = 0.547158766 + -2.722222222 x = 0.547158766 + -2.722222222 Combine like terms: 0.547158766 + -2.722222222 = -2.175063456 x = -2.175063456 Simplifying x = -2.175063456Subproblem 2
x + 2.722222222 = -0.547158766 Simplifying x + 2.722222222 = -0.547158766 Reorder the terms: 2.722222222 + x = -0.547158766 Solving 2.722222222 + x = -0.547158766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.722222222' to each side of the equation. 2.722222222 + -2.722222222 + x = -0.547158766 + -2.722222222 Combine like terms: 2.722222222 + -2.722222222 = 0.000000000 0.000000000 + x = -0.547158766 + -2.722222222 x = -0.547158766 + -2.722222222 Combine like terms: -0.547158766 + -2.722222222 = -3.269380988 x = -3.269380988 Simplifying x = -3.269380988Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.175063456, -3.269380988}
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