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Simplifying 4x2 + 17x + 2x = 10 Reorder the terms: 17x + 2x + 4x2 = 10 Combine like terms: 17x + 2x = 19x 19x + 4x2 = 10 Solving 19x + 4x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 19x + 4x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 19x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.5 + 4.75x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 4.75x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 4.75x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 4.75x + x2 = 0 + 2.5 4.75x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 4.75x + x2 = 2.5 The x term is 4.75x. Take half its coefficient (2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. 4.75x + 5.640625 + x2 = 2.5 + 5.640625 Reorder the terms: 5.640625 + 4.75x + x2 = 2.5 + 5.640625 Combine like terms: 2.5 + 5.640625 = 8.140625 5.640625 + 4.75x + x2 = 8.140625 Factor a perfect square on the left side: (x + 2.375)(x + 2.375) = 8.140625 Calculate the square root of the right side: 2.853178053 Break this problem into two subproblems by setting (x + 2.375) equal to 2.853178053 and -2.853178053.Subproblem 1
x + 2.375 = 2.853178053 Simplifying x + 2.375 = 2.853178053 Reorder the terms: 2.375 + x = 2.853178053 Solving 2.375 + x = 2.853178053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = 2.853178053 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = 2.853178053 + -2.375 x = 2.853178053 + -2.375 Combine like terms: 2.853178053 + -2.375 = 0.478178053 x = 0.478178053 Simplifying x = 0.478178053Subproblem 2
x + 2.375 = -2.853178053 Simplifying x + 2.375 = -2.853178053 Reorder the terms: 2.375 + x = -2.853178053 Solving 2.375 + x = -2.853178053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = -2.853178053 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = -2.853178053 + -2.375 x = -2.853178053 + -2.375 Combine like terms: -2.853178053 + -2.375 = -5.228178053 x = -5.228178053 Simplifying x = -5.228178053Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.478178053, -5.228178053}
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