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Simplifying 8x2 + 3x = 35 Reorder the terms: 3x + 8x2 = 35 Solving 3x + 8x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + 3x + 8x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.375 + 0.375x + x2 = 0 Move the constant term to the right: Add '4.375' to each side of the equation. -4.375 + 0.375x + 4.375 + x2 = 0 + 4.375 Reorder the terms: -4.375 + 4.375 + 0.375x + x2 = 0 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + 0.375x + x2 = 0 + 4.375 0.375x + x2 = 0 + 4.375 Combine like terms: 0 + 4.375 = 4.375 0.375x + x2 = 4.375 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 4.375 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 4.375 + 0.03515625 Combine like terms: 4.375 + 0.03515625 = 4.41015625 0.03515625 + 0.375x + x2 = 4.41015625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 4.41015625 Calculate the square root of the right side: 2.100037202 Break this problem into two subproblems by setting (x + 0.1875) equal to 2.100037202 and -2.100037202.Subproblem 1
x + 0.1875 = 2.100037202 Simplifying x + 0.1875 = 2.100037202 Reorder the terms: 0.1875 + x = 2.100037202 Solving 0.1875 + x = 2.100037202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 2.100037202 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 2.100037202 + -0.1875 x = 2.100037202 + -0.1875 Combine like terms: 2.100037202 + -0.1875 = 1.912537202 x = 1.912537202 Simplifying x = 1.912537202Subproblem 2
x + 0.1875 = -2.100037202 Simplifying x + 0.1875 = -2.100037202 Reorder the terms: 0.1875 + x = -2.100037202 Solving 0.1875 + x = -2.100037202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -2.100037202 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -2.100037202 + -0.1875 x = -2.100037202 + -0.1875 Combine like terms: -2.100037202 + -0.1875 = -2.287537202 x = -2.287537202 Simplifying x = -2.287537202Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.912537202, -2.287537202}
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