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Simplifying 4x2 + 5x = 10 Reorder the terms: 5x + 4x2 = 10 Solving 5x + 4x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 5x + 4x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.5 + 1.25x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 1.25x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 1.25x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 1.25x + x2 = 0 + 2.5 1.25x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 1.25x + x2 = 2.5 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 2.5 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 2.5 + 0.390625 Combine like terms: 2.5 + 0.390625 = 2.890625 0.390625 + 1.25x + x2 = 2.890625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 2.890625 Calculate the square root of the right side: 1.700183814 Break this problem into two subproblems by setting (x + 0.625) equal to 1.700183814 and -1.700183814.Subproblem 1
x + 0.625 = 1.700183814 Simplifying x + 0.625 = 1.700183814 Reorder the terms: 0.625 + x = 1.700183814 Solving 0.625 + x = 1.700183814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 1.700183814 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 1.700183814 + -0.625 x = 1.700183814 + -0.625 Combine like terms: 1.700183814 + -0.625 = 1.075183814 x = 1.075183814 Simplifying x = 1.075183814Subproblem 2
x + 0.625 = -1.700183814 Simplifying x + 0.625 = -1.700183814 Reorder the terms: 0.625 + x = -1.700183814 Solving 0.625 + x = -1.700183814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -1.700183814 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -1.700183814 + -0.625 x = -1.700183814 + -0.625 Combine like terms: -1.700183814 + -0.625 = -2.325183814 x = -2.325183814 Simplifying x = -2.325183814Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.075183814, -2.325183814}
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