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Simplifying -0.062x2 + 1.4647x + 5.2405 = 6 Reorder the terms: 5.2405 + 1.4647x + -0.062x2 = 6 Solving 5.2405 + 1.4647x + -0.062x2 = 6 Solving for variable 'x'. Reorder the terms: 5.2405 + -6 + 1.4647x + -0.062x2 = 6 + -6 Combine like terms: 5.2405 + -6 = -0.7595 -0.7595 + 1.4647x + -0.062x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -0.7595 + 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'. 12.25 + -23.62419355x + x2 = 0 Move the constant term to the right: Add '-12.25' to each side of the equation. 12.25 + -23.62419355x + -12.25 + x2 = 0 + -12.25 Reorder the terms: 12.25 + -12.25 + -23.62419355x + x2 = 0 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + -23.62419355x + x2 = 0 + -12.25 -23.62419355x + x2 = 0 + -12.25 Combine like terms: 0 + -12.25 = -12.25 -23.62419355x + x2 = -12.25 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 = -12.25 + 139.5256303 Reorder the terms: 139.5256303 + -23.62419355x + x2 = -12.25 + 139.5256303 Combine like terms: -12.25 + 139.5256303 = 127.2756303 139.5256303 + -23.62419355x + x2 = 127.2756303 Factor a perfect square on the left side: (x + -11.81209678)(x + -11.81209678) = 127.2756303 Calculate the square root of the right side: 11.281650159 Break this problem into two subproblems by setting (x + -11.81209678) equal to 11.281650159 and -11.281650159.Subproblem 1
x + -11.81209678 = 11.281650159 Simplifying x + -11.81209678 = 11.281650159 Reorder the terms: -11.81209678 + x = 11.281650159 Solving -11.81209678 + x = 11.281650159 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 = 11.281650159 + 11.81209678 Combine like terms: -11.81209678 + 11.81209678 = 0.00000000 0.00000000 + x = 11.281650159 + 11.81209678 x = 11.281650159 + 11.81209678 Combine like terms: 11.281650159 + 11.81209678 = 23.093746939 x = 23.093746939 Simplifying x = 23.093746939Subproblem 2
x + -11.81209678 = -11.281650159 Simplifying x + -11.81209678 = -11.281650159 Reorder the terms: -11.81209678 + x = -11.281650159 Solving -11.81209678 + x = -11.281650159 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 = -11.281650159 + 11.81209678 Combine like terms: -11.81209678 + 11.81209678 = 0.00000000 0.00000000 + x = -11.281650159 + 11.81209678 x = -11.281650159 + 11.81209678 Combine like terms: -11.281650159 + 11.81209678 = 0.530446621 x = 0.530446621 Simplifying x = 0.530446621Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.093746939, 0.530446621}
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