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Simplifying 7.5x2 + 0.64x + -894.72 = 0 Reorder the terms: -894.72 + 0.64x + 7.5x2 = 0 Solving -894.72 + 0.64x + 7.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7.5 the coefficient of the squared term: Divide each side by '7.5'. -119.296 + 0.08533333333x + x2 = 0 Move the constant term to the right: Add '119.296' to each side of the equation. -119.296 + 0.08533333333x + 119.296 + x2 = 0 + 119.296 Reorder the terms: -119.296 + 119.296 + 0.08533333333x + x2 = 0 + 119.296 Combine like terms: -119.296 + 119.296 = 0.000 0.000 + 0.08533333333x + x2 = 0 + 119.296 0.08533333333x + x2 = 0 + 119.296 Combine like terms: 0 + 119.296 = 119.296 0.08533333333x + x2 = 119.296 The x term is 0.08533333333x. Take half its coefficient (0.04266666667). Square it (0.001820444445) and add it to both sides. Add '0.001820444445' to each side of the equation. 0.08533333333x + 0.001820444445 + x2 = 119.296 + 0.001820444445 Reorder the terms: 0.001820444445 + 0.08533333333x + x2 = 119.296 + 0.001820444445 Combine like terms: 119.296 + 0.001820444445 = 119.297820444445 0.001820444445 + 0.08533333333x + x2 = 119.297820444445 Factor a perfect square on the left side: (x + 0.04266666667)(x + 0.04266666667) = 119.297820444445 Calculate the square root of the right side: 10.922354162 Break this problem into two subproblems by setting (x + 0.04266666667) equal to 10.922354162 and -10.922354162.Subproblem 1
x + 0.04266666667 = 10.922354162 Simplifying x + 0.04266666667 = 10.922354162 Reorder the terms: 0.04266666667 + x = 10.922354162 Solving 0.04266666667 + x = 10.922354162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04266666667' to each side of the equation. 0.04266666667 + -0.04266666667 + x = 10.922354162 + -0.04266666667 Combine like terms: 0.04266666667 + -0.04266666667 = 0.00000000000 0.00000000000 + x = 10.922354162 + -0.04266666667 x = 10.922354162 + -0.04266666667 Combine like terms: 10.922354162 + -0.04266666667 = 10.87968749533 x = 10.87968749533 Simplifying x = 10.87968749533Subproblem 2
x + 0.04266666667 = -10.922354162 Simplifying x + 0.04266666667 = -10.922354162 Reorder the terms: 0.04266666667 + x = -10.922354162 Solving 0.04266666667 + x = -10.922354162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04266666667' to each side of the equation. 0.04266666667 + -0.04266666667 + x = -10.922354162 + -0.04266666667 Combine like terms: 0.04266666667 + -0.04266666667 = 0.00000000000 0.00000000000 + x = -10.922354162 + -0.04266666667 x = -10.922354162 + -0.04266666667 Combine like terms: -10.922354162 + -0.04266666667 = -10.96502082867 x = -10.96502082867 Simplifying x = -10.96502082867Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.87968749533, -10.96502082867}
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