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Simplifying -0.062x2 + 1.4647x + 5.2405 = 9 Reorder the terms: 5.2405 + 1.4647x + -0.062x2 = 9 Solving 5.2405 + 1.4647x + -0.062x2 = 9 Solving for variable 'x'. Reorder the terms: 5.2405 + -9 + 1.4647x + -0.062x2 = 9 + -9 Combine like terms: 5.2405 + -9 = -3.7595 -3.7595 + 1.4647x + -0.062x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -3.7595 + 1.4647x + -0.062x2 = 0 Begin completing the square. Divide all terms by -0.062 the coefficient of the squared term: Divide each side by '-0.062'. 60.63709677 + -23.62419355x + x2 = 0 Move the constant term to the right: Add '-60.63709677' to each side of the equation. 60.63709677 + -23.62419355x + -60.63709677 + x2 = 0 + -60.63709677 Reorder the terms: 60.63709677 + -60.63709677 + -23.62419355x + x2 = 0 + -60.63709677 Combine like terms: 60.63709677 + -60.63709677 = 0.00000000 0.00000000 + -23.62419355x + x2 = 0 + -60.63709677 -23.62419355x + x2 = 0 + -60.63709677 Combine like terms: 0 + -60.63709677 = -60.63709677 -23.62419355x + x2 = -60.63709677 The x term is -23.62419355x. Take half its coefficient (-11.81209678). Square it (139.5256303) and add it to both sides. Add '139.5256303' to each side of the equation. -23.62419355x + 139.5256303 + x2 = -60.63709677 + 139.5256303 Reorder the terms: 139.5256303 + -23.62419355x + x2 = -60.63709677 + 139.5256303 Combine like terms: -60.63709677 + 139.5256303 = 78.88853353 139.5256303 + -23.62419355x + x2 = 78.88853353 Factor a perfect square on the left side: (x + -11.81209678)(x + -11.81209678) = 78.88853353 Calculate the square root of the right side: 8.881921725 Break this problem into two subproblems by setting (x + -11.81209678) equal to 8.881921725 and -8.881921725.Subproblem 1
x + -11.81209678 = 8.881921725 Simplifying x + -11.81209678 = 8.881921725 Reorder the terms: -11.81209678 + x = 8.881921725 Solving -11.81209678 + x = 8.881921725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.81209678' to each side of the equation. -11.81209678 + 11.81209678 + x = 8.881921725 + 11.81209678 Combine like terms: -11.81209678 + 11.81209678 = 0.00000000 0.00000000 + x = 8.881921725 + 11.81209678 x = 8.881921725 + 11.81209678 Combine like terms: 8.881921725 + 11.81209678 = 20.694018505 x = 20.694018505 Simplifying x = 20.694018505Subproblem 2
x + -11.81209678 = -8.881921725 Simplifying x + -11.81209678 = -8.881921725 Reorder the terms: -11.81209678 + x = -8.881921725 Solving -11.81209678 + x = -8.881921725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.81209678' to each side of the equation. -11.81209678 + 11.81209678 + x = -8.881921725 + 11.81209678 Combine like terms: -11.81209678 + 11.81209678 = 0.00000000 0.00000000 + x = -8.881921725 + 11.81209678 x = -8.881921725 + 11.81209678 Combine like terms: -8.881921725 + 11.81209678 = 2.930175055 x = 2.930175055 Simplifying x = 2.930175055Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.694018505, 2.930175055}
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