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Simplifying -0.062x2 + 1.4647x + 5.2405 = 7 Reorder the terms: 5.2405 + 1.4647x + -0.062x2 = 7 Solving 5.2405 + 1.4647x + -0.062x2 = 7 Solving for variable 'x'. Reorder the terms: 5.2405 + -7 + 1.4647x + -0.062x2 = 7 + -7 Combine like terms: 5.2405 + -7 = -1.7595 -1.7595 + 1.4647x + -0.062x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -1.7595 + 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'. 28.37903226 + -23.62419355x + x2 = 0 Move the constant term to the right: Add '-28.37903226' to each side of the equation. 28.37903226 + -23.62419355x + -28.37903226 + x2 = 0 + -28.37903226 Reorder the terms: 28.37903226 + -28.37903226 + -23.62419355x + x2 = 0 + -28.37903226 Combine like terms: 28.37903226 + -28.37903226 = 0.00000000 0.00000000 + -23.62419355x + x2 = 0 + -28.37903226 -23.62419355x + x2 = 0 + -28.37903226 Combine like terms: 0 + -28.37903226 = -28.37903226 -23.62419355x + x2 = -28.37903226 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 = -28.37903226 + 139.5256303 Reorder the terms: 139.5256303 + -23.62419355x + x2 = -28.37903226 + 139.5256303 Combine like terms: -28.37903226 + 139.5256303 = 111.14659804 139.5256303 + -23.62419355x + x2 = 111.14659804 Factor a perfect square on the left side: (x + -11.81209678)(x + -11.81209678) = 111.14659804 Calculate the square root of the right side: 10.542608692 Break this problem into two subproblems by setting (x + -11.81209678) equal to 10.542608692 and -10.542608692.Subproblem 1
x + -11.81209678 = 10.542608692 Simplifying x + -11.81209678 = 10.542608692 Reorder the terms: -11.81209678 + x = 10.542608692 Solving -11.81209678 + x = 10.542608692 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 = 10.542608692 + 11.81209678 Combine like terms: -11.81209678 + 11.81209678 = 0.00000000 0.00000000 + x = 10.542608692 + 11.81209678 x = 10.542608692 + 11.81209678 Combine like terms: 10.542608692 + 11.81209678 = 22.354705472 x = 22.354705472 Simplifying x = 22.354705472Subproblem 2
x + -11.81209678 = -10.542608692 Simplifying x + -11.81209678 = -10.542608692 Reorder the terms: -11.81209678 + x = -10.542608692 Solving -11.81209678 + x = -10.542608692 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 = -10.542608692 + 11.81209678 Combine like terms: -11.81209678 + 11.81209678 = 0.00000000 0.00000000 + x = -10.542608692 + 11.81209678 x = -10.542608692 + 11.81209678 Combine like terms: -10.542608692 + 11.81209678 = 1.269488088 x = 1.269488088 Simplifying x = 1.269488088Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.354705472, 1.269488088}
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