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Simplifying 72x2 + 150x + 25 = 0 Reorder the terms: 25 + 150x + 72x2 = 0 Solving 25 + 150x + 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'. 0.3472222222 + 2.083333333x + x2 = 0 Move the constant term to the right: Add '-0.3472222222' to each side of the equation. 0.3472222222 + 2.083333333x + -0.3472222222 + x2 = 0 + -0.3472222222 Reorder the terms: 0.3472222222 + -0.3472222222 + 2.083333333x + x2 = 0 + -0.3472222222 Combine like terms: 0.3472222222 + -0.3472222222 = 0.0000000000 0.0000000000 + 2.083333333x + x2 = 0 + -0.3472222222 2.083333333x + x2 = 0 + -0.3472222222 Combine like terms: 0 + -0.3472222222 = -0.3472222222 2.083333333x + x2 = -0.3472222222 The x term is 2.083333333x. Take half its coefficient (1.041666667). Square it (1.085069445) and add it to both sides. Add '1.085069445' to each side of the equation. 2.083333333x + 1.085069445 + x2 = -0.3472222222 + 1.085069445 Reorder the terms: 1.085069445 + 2.083333333x + x2 = -0.3472222222 + 1.085069445 Combine like terms: -0.3472222222 + 1.085069445 = 0.7378472228 1.085069445 + 2.083333333x + x2 = 0.7378472228 Factor a perfect square on the left side: (x + 1.041666667)(x + 1.041666667) = 0.7378472228 Calculate the square root of the right side: 0.858980339 Break this problem into two subproblems by setting (x + 1.041666667) equal to 0.858980339 and -0.858980339.Subproblem 1
x + 1.041666667 = 0.858980339 Simplifying x + 1.041666667 = 0.858980339 Reorder the terms: 1.041666667 + x = 0.858980339 Solving 1.041666667 + x = 0.858980339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.041666667' to each side of the equation. 1.041666667 + -1.041666667 + x = 0.858980339 + -1.041666667 Combine like terms: 1.041666667 + -1.041666667 = 0.000000000 0.000000000 + x = 0.858980339 + -1.041666667 x = 0.858980339 + -1.041666667 Combine like terms: 0.858980339 + -1.041666667 = -0.182686328 x = -0.182686328 Simplifying x = -0.182686328Subproblem 2
x + 1.041666667 = -0.858980339 Simplifying x + 1.041666667 = -0.858980339 Reorder the terms: 1.041666667 + x = -0.858980339 Solving 1.041666667 + x = -0.858980339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.041666667' to each side of the equation. 1.041666667 + -1.041666667 + x = -0.858980339 + -1.041666667 Combine like terms: 1.041666667 + -1.041666667 = 0.000000000 0.000000000 + x = -0.858980339 + -1.041666667 x = -0.858980339 + -1.041666667 Combine like terms: -0.858980339 + -1.041666667 = -1.900647006 x = -1.900647006 Simplifying x = -1.900647006Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.182686328, -1.900647006}
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