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Simplifying 4x2 + -10x = 35 Reorder the terms: -10x + 4x2 = 35 Solving -10x + 4x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + -10x + 4x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + -10x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.75 + -2.5x + x2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + -2.5x + 8.75 + x2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + -2.5x + x2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + -2.5x + x2 = 0 + 8.75 -2.5x + x2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 -2.5x + x2 = 8.75 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 8.75 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 8.75 + 1.5625 Combine like terms: 8.75 + 1.5625 = 10.3125 1.5625 + -2.5x + x2 = 10.3125 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 10.3125 Calculate the square root of the right side: 3.211308145 Break this problem into two subproblems by setting (x + -1.25) equal to 3.211308145 and -3.211308145.Subproblem 1
x + -1.25 = 3.211308145 Simplifying x + -1.25 = 3.211308145 Reorder the terms: -1.25 + x = 3.211308145 Solving -1.25 + x = 3.211308145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 3.211308145 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 3.211308145 + 1.25 x = 3.211308145 + 1.25 Combine like terms: 3.211308145 + 1.25 = 4.461308145 x = 4.461308145 Simplifying x = 4.461308145Subproblem 2
x + -1.25 = -3.211308145 Simplifying x + -1.25 = -3.211308145 Reorder the terms: -1.25 + x = -3.211308145 Solving -1.25 + x = -3.211308145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -3.211308145 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -3.211308145 + 1.25 x = -3.211308145 + 1.25 Combine like terms: -3.211308145 + 1.25 = -1.961308145 x = -1.961308145 Simplifying x = -1.961308145Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.461308145, -1.961308145}
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