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Simplifying x + (4x)(4x + -23) = 562 Remove parenthesis around (4x) x + 4x(4x + -23) = 562 Reorder the terms: x + 4x(-23 + 4x) = 562 x + (-23 * 4x + 4x * 4x) = 562 x + (-92x + 16x2) = 562 Combine like terms: x + -92x = -91x -91x + 16x2 = 562 Solving -91x + 16x2 = 562 Solving for variable 'x'. Reorder the terms: -562 + -91x + 16x2 = 562 + -562 Combine like terms: 562 + -562 = 0 -562 + -91x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -35.125 + -5.6875x + x2 = 0 Move the constant term to the right: Add '35.125' to each side of the equation. -35.125 + -5.6875x + 35.125 + x2 = 0 + 35.125 Reorder the terms: -35.125 + 35.125 + -5.6875x + x2 = 0 + 35.125 Combine like terms: -35.125 + 35.125 = 0.000 0.000 + -5.6875x + x2 = 0 + 35.125 -5.6875x + x2 = 0 + 35.125 Combine like terms: 0 + 35.125 = 35.125 -5.6875x + x2 = 35.125 The x term is -5.6875x. Take half its coefficient (-2.84375). Square it (8.086914063) and add it to both sides. Add '8.086914063' to each side of the equation. -5.6875x + 8.086914063 + x2 = 35.125 + 8.086914063 Reorder the terms: 8.086914063 + -5.6875x + x2 = 35.125 + 8.086914063 Combine like terms: 35.125 + 8.086914063 = 43.211914063 8.086914063 + -5.6875x + x2 = 43.211914063 Factor a perfect square on the left side: (x + -2.84375)(x + -2.84375) = 43.211914063 Calculate the square root of the right side: 6.573576961 Break this problem into two subproblems by setting (x + -2.84375) equal to 6.573576961 and -6.573576961.Subproblem 1
x + -2.84375 = 6.573576961 Simplifying x + -2.84375 = 6.573576961 Reorder the terms: -2.84375 + x = 6.573576961 Solving -2.84375 + x = 6.573576961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.84375' to each side of the equation. -2.84375 + 2.84375 + x = 6.573576961 + 2.84375 Combine like terms: -2.84375 + 2.84375 = 0.00000 0.00000 + x = 6.573576961 + 2.84375 x = 6.573576961 + 2.84375 Combine like terms: 6.573576961 + 2.84375 = 9.417326961 x = 9.417326961 Simplifying x = 9.417326961Subproblem 2
x + -2.84375 = -6.573576961 Simplifying x + -2.84375 = -6.573576961 Reorder the terms: -2.84375 + x = -6.573576961 Solving -2.84375 + x = -6.573576961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.84375' to each side of the equation. -2.84375 + 2.84375 + x = -6.573576961 + 2.84375 Combine like terms: -2.84375 + 2.84375 = 0.00000 0.00000 + x = -6.573576961 + 2.84375 x = -6.573576961 + 2.84375 Combine like terms: -6.573576961 + 2.84375 = -3.729826961 x = -3.729826961 Simplifying x = -3.729826961Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.417326961, -3.729826961}
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