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Simplifying 63x = 16x2 + 4x + 1 Reorder the terms: 63x = 1 + 4x + 16x2 Solving 63x = 1 + 4x + 16x2 Solving for variable 'x'. Reorder the terms: -1 + 63x + -4x + -16x2 = 1 + 4x + 16x2 + -1 + -4x + -16x2 Combine like terms: 63x + -4x = 59x -1 + 59x + -16x2 = 1 + 4x + 16x2 + -1 + -4x + -16x2 Reorder the terms: -1 + 59x + -16x2 = 1 + -1 + 4x + -4x + 16x2 + -16x2 Combine like terms: 1 + -1 = 0 -1 + 59x + -16x2 = 0 + 4x + -4x + 16x2 + -16x2 -1 + 59x + -16x2 = 4x + -4x + 16x2 + -16x2 Combine like terms: 4x + -4x = 0 -1 + 59x + -16x2 = 0 + 16x2 + -16x2 -1 + 59x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -1 + 59x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.0625 + -3.6875x + x2 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + -3.6875x + -0.0625 + x2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + -3.6875x + x2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + -3.6875x + x2 = 0 + -0.0625 -3.6875x + x2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 -3.6875x + x2 = -0.0625 The x term is -3.6875x. Take half its coefficient (-1.84375). Square it (3.399414063) and add it to both sides. Add '3.399414063' to each side of the equation. -3.6875x + 3.399414063 + x2 = -0.0625 + 3.399414063 Reorder the terms: 3.399414063 + -3.6875x + x2 = -0.0625 + 3.399414063 Combine like terms: -0.0625 + 3.399414063 = 3.336914063 3.399414063 + -3.6875x + x2 = 3.336914063 Factor a perfect square on the left side: (x + -1.84375)(x + -1.84375) = 3.336914063 Calculate the square root of the right side: 1.826722218 Break this problem into two subproblems by setting (x + -1.84375) equal to 1.826722218 and -1.826722218.Subproblem 1
x + -1.84375 = 1.826722218 Simplifying x + -1.84375 = 1.826722218 Reorder the terms: -1.84375 + x = 1.826722218 Solving -1.84375 + x = 1.826722218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.84375' to each side of the equation. -1.84375 + 1.84375 + x = 1.826722218 + 1.84375 Combine like terms: -1.84375 + 1.84375 = 0.00000 0.00000 + x = 1.826722218 + 1.84375 x = 1.826722218 + 1.84375 Combine like terms: 1.826722218 + 1.84375 = 3.670472218 x = 3.670472218 Simplifying x = 3.670472218Subproblem 2
x + -1.84375 = -1.826722218 Simplifying x + -1.84375 = -1.826722218 Reorder the terms: -1.84375 + x = -1.826722218 Solving -1.84375 + x = -1.826722218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.84375' to each side of the equation. -1.84375 + 1.84375 + x = -1.826722218 + 1.84375 Combine like terms: -1.84375 + 1.84375 = 0.00000 0.00000 + x = -1.826722218 + 1.84375 x = -1.826722218 + 1.84375 Combine like terms: -1.826722218 + 1.84375 = 0.017027782 x = 0.017027782 Simplifying x = 0.017027782Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.670472218, 0.017027782}
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