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Simplifying -72x2 + 95x + 88 = 0 Reorder the terms: 88 + 95x + -72x2 = 0 Solving 88 + 95x + -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'. -1.222222222 + -1.319444444x + x2 = 0 Move the constant term to the right: Add '1.222222222' to each side of the equation. -1.222222222 + -1.319444444x + 1.222222222 + x2 = 0 + 1.222222222 Reorder the terms: -1.222222222 + 1.222222222 + -1.319444444x + x2 = 0 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + -1.319444444x + x2 = 0 + 1.222222222 -1.319444444x + x2 = 0 + 1.222222222 Combine like terms: 0 + 1.222222222 = 1.222222222 -1.319444444x + x2 = 1.222222222 The x term is -1.319444444x. Take half its coefficient (-0.659722222). Square it (0.4352334102) and add it to both sides. Add '0.4352334102' to each side of the equation. -1.319444444x + 0.4352334102 + x2 = 1.222222222 + 0.4352334102 Reorder the terms: 0.4352334102 + -1.319444444x + x2 = 1.222222222 + 0.4352334102 Combine like terms: 1.222222222 + 0.4352334102 = 1.6574556322 0.4352334102 + -1.319444444x + x2 = 1.6574556322 Factor a perfect square on the left side: (x + -0.659722222)(x + -0.659722222) = 1.6574556322 Calculate the square root of the right side: 1.287422088 Break this problem into two subproblems by setting (x + -0.659722222) equal to 1.287422088 and -1.287422088.Subproblem 1
x + -0.659722222 = 1.287422088 Simplifying x + -0.659722222 = 1.287422088 Reorder the terms: -0.659722222 + x = 1.287422088 Solving -0.659722222 + x = 1.287422088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.659722222' to each side of the equation. -0.659722222 + 0.659722222 + x = 1.287422088 + 0.659722222 Combine like terms: -0.659722222 + 0.659722222 = 0.000000000 0.000000000 + x = 1.287422088 + 0.659722222 x = 1.287422088 + 0.659722222 Combine like terms: 1.287422088 + 0.659722222 = 1.94714431 x = 1.94714431 Simplifying x = 1.94714431Subproblem 2
x + -0.659722222 = -1.287422088 Simplifying x + -0.659722222 = -1.287422088 Reorder the terms: -0.659722222 + x = -1.287422088 Solving -0.659722222 + x = -1.287422088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.659722222' to each side of the equation. -0.659722222 + 0.659722222 + x = -1.287422088 + 0.659722222 Combine like terms: -0.659722222 + 0.659722222 = 0.000000000 0.000000000 + x = -1.287422088 + 0.659722222 x = -1.287422088 + 0.659722222 Combine like terms: -1.287422088 + 0.659722222 = -0.627699866 x = -0.627699866 Simplifying x = -0.627699866Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.94714431, -0.627699866}
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