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Simplifying 184 = (2x + -7)(x + 4) Reorder the terms: 184 = (-7 + 2x)(x + 4) Reorder the terms: 184 = (-7 + 2x)(4 + x) Multiply (-7 + 2x) * (4 + x) 184 = (-7(4 + x) + 2x * (4 + x)) 184 = ((4 * -7 + x * -7) + 2x * (4 + x)) 184 = ((-28 + -7x) + 2x * (4 + x)) 184 = (-28 + -7x + (4 * 2x + x * 2x)) 184 = (-28 + -7x + (8x + 2x2)) Combine like terms: -7x + 8x = 1x 184 = (-28 + 1x + 2x2) Solving 184 = -28 + 1x + 2x2 Solving for variable 'x'. Combine like terms: 184 + 28 = 212 212 + -1x + -2x2 = -28 + 1x + 2x2 + 28 + -1x + -2x2 Reorder the terms: 212 + -1x + -2x2 = -28 + 28 + 1x + -1x + 2x2 + -2x2 Combine like terms: -28 + 28 = 0 212 + -1x + -2x2 = 0 + 1x + -1x + 2x2 + -2x2 212 + -1x + -2x2 = 1x + -1x + 2x2 + -2x2 Combine like terms: 1x + -1x = 0 212 + -1x + -2x2 = 0 + 2x2 + -2x2 212 + -1x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 212 + -1x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -106 + 0.5x + x2 = 0 Move the constant term to the right: Add '106' to each side of the equation. -106 + 0.5x + 106 + x2 = 0 + 106 Reorder the terms: -106 + 106 + 0.5x + x2 = 0 + 106 Combine like terms: -106 + 106 = 0 0 + 0.5x + x2 = 0 + 106 0.5x + x2 = 0 + 106 Combine like terms: 0 + 106 = 106 0.5x + x2 = 106 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 106 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 106 + 0.0625 Combine like terms: 106 + 0.0625 = 106.0625 0.0625 + 0.5x + x2 = 106.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 106.0625 Calculate the square root of the right side: 10.298664962 Break this problem into two subproblems by setting (x + 0.25) equal to 10.298664962 and -10.298664962.Subproblem 1
x + 0.25 = 10.298664962 Simplifying x + 0.25 = 10.298664962 Reorder the terms: 0.25 + x = 10.298664962 Solving 0.25 + x = 10.298664962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 10.298664962 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 10.298664962 + -0.25 x = 10.298664962 + -0.25 Combine like terms: 10.298664962 + -0.25 = 10.048664962 x = 10.048664962 Simplifying x = 10.048664962Subproblem 2
x + 0.25 = -10.298664962 Simplifying x + 0.25 = -10.298664962 Reorder the terms: 0.25 + x = -10.298664962 Solving 0.25 + x = -10.298664962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -10.298664962 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -10.298664962 + -0.25 x = -10.298664962 + -0.25 Combine like terms: -10.298664962 + -0.25 = -10.548664962 x = -10.548664962 Simplifying x = -10.548664962Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.048664962, -10.548664962}
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