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Simplifying 9x(8x + -7) + 8x + 7 = 0 Reorder the terms: 9x(-7 + 8x) + 8x + 7 = 0 (-7 * 9x + 8x * 9x) + 8x + 7 = 0 (-63x + 72x2) + 8x + 7 = 0 Reorder the terms: 7 + -63x + 8x + 72x2 = 0 Combine like terms: -63x + 8x = -55x 7 + -55x + 72x2 = 0 Solving 7 + -55x + 72x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 72 the coefficient of the squared term: Divide each side by '72'. 0.09722222222 + -0.7638888889x + x2 = 0 Move the constant term to the right: Add '-0.09722222222' to each side of the equation. 0.09722222222 + -0.7638888889x + -0.09722222222 + x2 = 0 + -0.09722222222 Reorder the terms: 0.09722222222 + -0.09722222222 + -0.7638888889x + x2 = 0 + -0.09722222222 Combine like terms: 0.09722222222 + -0.09722222222 = 0.00000000000 0.00000000000 + -0.7638888889x + x2 = 0 + -0.09722222222 -0.7638888889x + x2 = 0 + -0.09722222222 Combine like terms: 0 + -0.09722222222 = -0.09722222222 -0.7638888889x + x2 = -0.09722222222 The x term is -0.7638888889x. Take half its coefficient (-0.3819444445). Square it (0.1458815587) and add it to both sides. Add '0.1458815587' to each side of the equation. -0.7638888889x + 0.1458815587 + x2 = -0.09722222222 + 0.1458815587 Reorder the terms: 0.1458815587 + -0.7638888889x + x2 = -0.09722222222 + 0.1458815587 Combine like terms: -0.09722222222 + 0.1458815587 = 0.04865933648 0.1458815587 + -0.7638888889x + x2 = 0.04865933648 Factor a perfect square on the left side: (x + -0.3819444445)(x + -0.3819444445) = 0.04865933648 Calculate the square root of the right side: 0.220588614 Break this problem into two subproblems by setting (x + -0.3819444445) equal to 0.220588614 and -0.220588614.Subproblem 1
x + -0.3819444445 = 0.220588614 Simplifying x + -0.3819444445 = 0.220588614 Reorder the terms: -0.3819444445 + x = 0.220588614 Solving -0.3819444445 + x = 0.220588614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3819444445' to each side of the equation. -0.3819444445 + 0.3819444445 + x = 0.220588614 + 0.3819444445 Combine like terms: -0.3819444445 + 0.3819444445 = 0.0000000000 0.0000000000 + x = 0.220588614 + 0.3819444445 x = 0.220588614 + 0.3819444445 Combine like terms: 0.220588614 + 0.3819444445 = 0.6025330585 x = 0.6025330585 Simplifying x = 0.6025330585Subproblem 2
x + -0.3819444445 = -0.220588614 Simplifying x + -0.3819444445 = -0.220588614 Reorder the terms: -0.3819444445 + x = -0.220588614 Solving -0.3819444445 + x = -0.220588614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3819444445' to each side of the equation. -0.3819444445 + 0.3819444445 + x = -0.220588614 + 0.3819444445 Combine like terms: -0.3819444445 + 0.3819444445 = 0.0000000000 0.0000000000 + x = -0.220588614 + 0.3819444445 x = -0.220588614 + 0.3819444445 Combine like terms: -0.220588614 + 0.3819444445 = 0.1613558305 x = 0.1613558305 Simplifying x = 0.1613558305Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6025330585, 0.1613558305}
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