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Simplifying 15x2 + -80x + 99 = 0 Reorder the terms: 99 + -80x + 15x2 = 0 Solving 99 + -80x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 6.6 + -5.333333333x + x2 = 0 Move the constant term to the right: Add '-6.6' to each side of the equation. 6.6 + -5.333333333x + -6.6 + x2 = 0 + -6.6 Reorder the terms: 6.6 + -6.6 + -5.333333333x + x2 = 0 + -6.6 Combine like terms: 6.6 + -6.6 = 0.0 0.0 + -5.333333333x + x2 = 0 + -6.6 -5.333333333x + x2 = 0 + -6.6 Combine like terms: 0 + -6.6 = -6.6 -5.333333333x + x2 = -6.6 The x term is -5.333333333x. Take half its coefficient (-2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. -5.333333333x + 7.111111113 + x2 = -6.6 + 7.111111113 Reorder the terms: 7.111111113 + -5.333333333x + x2 = -6.6 + 7.111111113 Combine like terms: -6.6 + 7.111111113 = 0.511111113 7.111111113 + -5.333333333x + x2 = 0.511111113 Factor a perfect square on the left side: (x + -2.666666667)(x + -2.666666667) = 0.511111113 Calculate the square root of the right side: 0.714920354 Break this problem into two subproblems by setting (x + -2.666666667) equal to 0.714920354 and -0.714920354.Subproblem 1
x + -2.666666667 = 0.714920354 Simplifying x + -2.666666667 = 0.714920354 Reorder the terms: -2.666666667 + x = 0.714920354 Solving -2.666666667 + x = 0.714920354 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + x = 0.714920354 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = 0.714920354 + 2.666666667 x = 0.714920354 + 2.666666667 Combine like terms: 0.714920354 + 2.666666667 = 3.381587021 x = 3.381587021 Simplifying x = 3.381587021Subproblem 2
x + -2.666666667 = -0.714920354 Simplifying x + -2.666666667 = -0.714920354 Reorder the terms: -2.666666667 + x = -0.714920354 Solving -2.666666667 + x = -0.714920354 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + x = -0.714920354 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = -0.714920354 + 2.666666667 x = -0.714920354 + 2.666666667 Combine like terms: -0.714920354 + 2.666666667 = 1.951746313 x = 1.951746313 Simplifying x = 1.951746313Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.381587021, 1.951746313}
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