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Simplifying 350 = (4x + 1)(x + 1) Reorder the terms: 350 = (1 + 4x)(x + 1) Reorder the terms: 350 = (1 + 4x)(1 + x) Multiply (1 + 4x) * (1 + x) 350 = (1(1 + x) + 4x * (1 + x)) 350 = ((1 * 1 + x * 1) + 4x * (1 + x)) 350 = ((1 + 1x) + 4x * (1 + x)) 350 = (1 + 1x + (1 * 4x + x * 4x)) 350 = (1 + 1x + (4x + 4x2)) Combine like terms: 1x + 4x = 5x 350 = (1 + 5x + 4x2) Solving 350 = 1 + 5x + 4x2 Solving for variable 'x'. Combine like terms: 350 + -1 = 349 349 + -5x + -4x2 = 1 + 5x + 4x2 + -1 + -5x + -4x2 Reorder the terms: 349 + -5x + -4x2 = 1 + -1 + 5x + -5x + 4x2 + -4x2 Combine like terms: 1 + -1 = 0 349 + -5x + -4x2 = 0 + 5x + -5x + 4x2 + -4x2 349 + -5x + -4x2 = 5x + -5x + 4x2 + -4x2 Combine like terms: 5x + -5x = 0 349 + -5x + -4x2 = 0 + 4x2 + -4x2 349 + -5x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 349 + -5x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -87.25 + 1.25x + x2 = 0 Move the constant term to the right: Add '87.25' to each side of the equation. -87.25 + 1.25x + 87.25 + x2 = 0 + 87.25 Reorder the terms: -87.25 + 87.25 + 1.25x + x2 = 0 + 87.25 Combine like terms: -87.25 + 87.25 = 0.00 0.00 + 1.25x + x2 = 0 + 87.25 1.25x + x2 = 0 + 87.25 Combine like terms: 0 + 87.25 = 87.25 1.25x + x2 = 87.25 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 = 87.25 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 87.25 + 0.390625 Combine like terms: 87.25 + 0.390625 = 87.640625 0.390625 + 1.25x + x2 = 87.640625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 87.640625 Calculate the square root of the right side: 9.361657172 Break this problem into two subproblems by setting (x + 0.625) equal to 9.361657172 and -9.361657172.Subproblem 1
x + 0.625 = 9.361657172 Simplifying x + 0.625 = 9.361657172 Reorder the terms: 0.625 + x = 9.361657172 Solving 0.625 + x = 9.361657172 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 = 9.361657172 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 9.361657172 + -0.625 x = 9.361657172 + -0.625 Combine like terms: 9.361657172 + -0.625 = 8.736657172 x = 8.736657172 Simplifying x = 8.736657172Subproblem 2
x + 0.625 = -9.361657172 Simplifying x + 0.625 = -9.361657172 Reorder the terms: 0.625 + x = -9.361657172 Solving 0.625 + x = -9.361657172 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 = -9.361657172 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -9.361657172 + -0.625 x = -9.361657172 + -0.625 Combine like terms: -9.361657172 + -0.625 = -9.986657172 x = -9.986657172 Simplifying x = -9.986657172Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.736657172, -9.986657172}
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