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Simplifying -0.062x2 + 1.4647x + 5.2405 = 8 Reorder the terms: 5.2405 + 1.4647x + -0.062x2 = 8 Solving 5.2405 + 1.4647x + -0.062x2 = 8 Solving for variable 'x'. Reorder the terms: 5.2405 + -8 + 1.4647x + -0.062x2 = 8 + -8 Combine like terms: 5.2405 + -8 = -2.7595 -2.7595 + 1.4647x + -0.062x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -2.7595 + 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'. 44.50806452 + -23.62419355x + x2 = 0 Move the constant term to the right: Add '-44.50806452' to each side of the equation. 44.50806452 + -23.62419355x + -44.50806452 + x2 = 0 + -44.50806452 Reorder the terms: 44.50806452 + -44.50806452 + -23.62419355x + x2 = 0 + -44.50806452 Combine like terms: 44.50806452 + -44.50806452 = 0.00000000 0.00000000 + -23.62419355x + x2 = 0 + -44.50806452 -23.62419355x + x2 = 0 + -44.50806452 Combine like terms: 0 + -44.50806452 = -44.50806452 -23.62419355x + x2 = -44.50806452 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 = -44.50806452 + 139.5256303 Reorder the terms: 139.5256303 + -23.62419355x + x2 = -44.50806452 + 139.5256303 Combine like terms: -44.50806452 + 139.5256303 = 95.01756578 139.5256303 + -23.62419355x + x2 = 95.01756578 Factor a perfect square on the left side: (x + -11.81209678)(x + -11.81209678) = 95.01756578 Calculate the square root of the right side: 9.747695409 Break this problem into two subproblems by setting (x + -11.81209678) equal to 9.747695409 and -9.747695409.Subproblem 1
x + -11.81209678 = 9.747695409 Simplifying x + -11.81209678 = 9.747695409 Reorder the terms: -11.81209678 + x = 9.747695409 Solving -11.81209678 + x = 9.747695409 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 = 9.747695409 + 11.81209678 Combine like terms: -11.81209678 + 11.81209678 = 0.00000000 0.00000000 + x = 9.747695409 + 11.81209678 x = 9.747695409 + 11.81209678 Combine like terms: 9.747695409 + 11.81209678 = 21.559792189 x = 21.559792189 Simplifying x = 21.559792189Subproblem 2
x + -11.81209678 = -9.747695409 Simplifying x + -11.81209678 = -9.747695409 Reorder the terms: -11.81209678 + x = -9.747695409 Solving -11.81209678 + x = -9.747695409 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 = -9.747695409 + 11.81209678 Combine like terms: -11.81209678 + 11.81209678 = 0.00000000 0.00000000 + x = -9.747695409 + 11.81209678 x = -9.747695409 + 11.81209678 Combine like terms: -9.747695409 + 11.81209678 = 2.064401371 x = 2.064401371 Simplifying x = 2.064401371Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.559792189, 2.064401371}
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