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Simplifying 4x2 + 20 = 10 + 35x Reorder the terms: 20 + 4x2 = 10 + 35x Solving 20 + 4x2 = 10 + 35x Solving for variable 'x'. Reorder the terms: 20 + -10 + -35x + 4x2 = 10 + 35x + -10 + -35x Combine like terms: 20 + -10 = 10 10 + -35x + 4x2 = 10 + 35x + -10 + -35x Reorder the terms: 10 + -35x + 4x2 = 10 + -10 + 35x + -35x Combine like terms: 10 + -10 = 0 10 + -35x + 4x2 = 0 + 35x + -35x 10 + -35x + 4x2 = 35x + -35x Combine like terms: 35x + -35x = 0 10 + -35x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.5 + -8.75x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -8.75x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -8.75x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -8.75x + x2 = 0 + -2.5 -8.75x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -8.75x + x2 = -2.5 The x term is -8.75x. Take half its coefficient (-4.375). Square it (19.140625) and add it to both sides. Add '19.140625' to each side of the equation. -8.75x + 19.140625 + x2 = -2.5 + 19.140625 Reorder the terms: 19.140625 + -8.75x + x2 = -2.5 + 19.140625 Combine like terms: -2.5 + 19.140625 = 16.640625 19.140625 + -8.75x + x2 = 16.640625 Factor a perfect square on the left side: (x + -4.375)(x + -4.375) = 16.640625 Calculate the square root of the right side: 4.079292218 Break this problem into two subproblems by setting (x + -4.375) equal to 4.079292218 and -4.079292218.Subproblem 1
x + -4.375 = 4.079292218 Simplifying x + -4.375 = 4.079292218 Reorder the terms: -4.375 + x = 4.079292218 Solving -4.375 + x = 4.079292218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = 4.079292218 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = 4.079292218 + 4.375 x = 4.079292218 + 4.375 Combine like terms: 4.079292218 + 4.375 = 8.454292218 x = 8.454292218 Simplifying x = 8.454292218Subproblem 2
x + -4.375 = -4.079292218 Simplifying x + -4.375 = -4.079292218 Reorder the terms: -4.375 + x = -4.079292218 Solving -4.375 + x = -4.079292218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = -4.079292218 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = -4.079292218 + 4.375 x = -4.079292218 + 4.375 Combine like terms: -4.079292218 + 4.375 = 0.295707782 x = 0.295707782 Simplifying x = 0.295707782Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.454292218, 0.295707782}
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