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Simplifying 4x2 + 6x = 35 Reorder the terms: 6x + 4x2 = 35 Solving 6x + 4x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + 6x + 4x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.75 + 1.5x + x2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + 1.5x + 8.75 + x2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + 1.5x + x2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + 1.5x + x2 = 0 + 8.75 1.5x + x2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 1.5x + x2 = 8.75 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 8.75 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 8.75 + 0.5625 Combine like terms: 8.75 + 0.5625 = 9.3125 0.5625 + 1.5x + x2 = 9.3125 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 9.3125 Calculate the square root of the right side: 3.051638904 Break this problem into two subproblems by setting (x + 0.75) equal to 3.051638904 and -3.051638904.Subproblem 1
x + 0.75 = 3.051638904 Simplifying x + 0.75 = 3.051638904 Reorder the terms: 0.75 + x = 3.051638904 Solving 0.75 + x = 3.051638904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 3.051638904 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 3.051638904 + -0.75 x = 3.051638904 + -0.75 Combine like terms: 3.051638904 + -0.75 = 2.301638904 x = 2.301638904 Simplifying x = 2.301638904Subproblem 2
x + 0.75 = -3.051638904 Simplifying x + 0.75 = -3.051638904 Reorder the terms: 0.75 + x = -3.051638904 Solving 0.75 + x = -3.051638904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -3.051638904 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -3.051638904 + -0.75 x = -3.051638904 + -0.75 Combine like terms: -3.051638904 + -0.75 = -3.801638904 x = -3.801638904 Simplifying x = -3.801638904Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.301638904, -3.801638904}
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