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Simplifying 400 = (4x + 7)(x) Reorder the terms: 400 = (7 + 4x)(x) Reorder the terms for easier multiplication: 400 = x(7 + 4x) 400 = (7 * x + 4x * x) 400 = (7x + 4x2) Solving 400 = 7x + 4x2 Solving for variable 'x'. Reorder the terms: 400 + -7x + -4x2 = 7x + -7x + 4x2 + -4x2 Combine like terms: 7x + -7x = 0 400 + -7x + -4x2 = 0 + 4x2 + -4x2 400 + -7x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 400 + -7x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -100 + 1.75x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 1.75x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 1.75x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 1.75x + x2 = 0 + 100 1.75x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 1.75x + x2 = 100 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 100 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 100 + 0.765625 Combine like terms: 100 + 0.765625 = 100.765625 0.765625 + 1.75x + x2 = 100.765625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 100.765625 Calculate the square root of the right side: 10.038208256 Break this problem into two subproblems by setting (x + 0.875) equal to 10.038208256 and -10.038208256.Subproblem 1
x + 0.875 = 10.038208256 Simplifying x + 0.875 = 10.038208256 Reorder the terms: 0.875 + x = 10.038208256 Solving 0.875 + x = 10.038208256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 10.038208256 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 10.038208256 + -0.875 x = 10.038208256 + -0.875 Combine like terms: 10.038208256 + -0.875 = 9.163208256 x = 9.163208256 Simplifying x = 9.163208256Subproblem 2
x + 0.875 = -10.038208256 Simplifying x + 0.875 = -10.038208256 Reorder the terms: 0.875 + x = -10.038208256 Solving 0.875 + x = -10.038208256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -10.038208256 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -10.038208256 + -0.875 x = -10.038208256 + -0.875 Combine like terms: -10.038208256 + -0.875 = -10.913208256 x = -10.913208256 Simplifying x = -10.913208256Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.163208256, -10.913208256}
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