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Simplifying 4x2 + 5x = 100 Reorder the terms: 5x + 4x2 = 100 Solving 5x + 4x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 5x + 4x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -25 + 1.25x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 1.25x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 1.25x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 1.25x + x2 = 0 + 25 1.25x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 1.25x + x2 = 25 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 = 25 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 25 + 0.390625 Combine like terms: 25 + 0.390625 = 25.390625 0.390625 + 1.25x + x2 = 25.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 25.390625 Calculate the square root of the right side: 5.038911093 Break this problem into two subproblems by setting (x + 0.625) equal to 5.038911093 and -5.038911093.Subproblem 1
x + 0.625 = 5.038911093 Simplifying x + 0.625 = 5.038911093 Reorder the terms: 0.625 + x = 5.038911093 Solving 0.625 + x = 5.038911093 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 = 5.038911093 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 5.038911093 + -0.625 x = 5.038911093 + -0.625 Combine like terms: 5.038911093 + -0.625 = 4.413911093 x = 4.413911093 Simplifying x = 4.413911093Subproblem 2
x + 0.625 = -5.038911093 Simplifying x + 0.625 = -5.038911093 Reorder the terms: 0.625 + x = -5.038911093 Solving 0.625 + x = -5.038911093 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 = -5.038911093 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -5.038911093 + -0.625 x = -5.038911093 + -0.625 Combine like terms: -5.038911093 + -0.625 = -5.663911093 x = -5.663911093 Simplifying x = -5.663911093Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.413911093, -5.663911093}
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