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Simplifying 4x3(7x3 + -16) + 7 = 0 Reorder the terms: 4x3(-16 + 7x3) + 7 = 0 (-16 * 4x3 + 7x3 * 4x3) + 7 = 0 (-64x3 + 28x6) + 7 = 0 Reorder the terms: 7 + -64x3 + 28x6 = 0 Solving 7 + -64x3 + 28x6 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. 0.25 + -2.285714286x3 + x6 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -2.285714286x3 + -0.25 + x6 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -2.285714286x3 + x6 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -2.285714286x3 + x6 = 0 + -0.25 -2.285714286x3 + x6 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -2.285714286x3 + x6 = -0.25 The x term is -2.285714286x3. Take half its coefficient (-1.142857143). Square it (1.306122449) and add it to both sides. Add '1.306122449' to each side of the equation. -2.285714286x3 + 1.306122449 + x6 = -0.25 + 1.306122449 Reorder the terms: 1.306122449 + -2.285714286x3 + x6 = -0.25 + 1.306122449 Combine like terms: -0.25 + 1.306122449 = 1.056122449 1.306122449 + -2.285714286x3 + x6 = 1.056122449 Factor a perfect square on the left side: (x3 + -1.142857143)(x3 + -1.142857143) = 1.056122449 Calculate the square root of the right side: 1.027678184 Break this problem into two subproblems by setting (x3 + -1.142857143) equal to 1.027678184 and -1.027678184.Subproblem 1
x3 + -1.142857143 = 1.027678184 Simplifying x3 + -1.142857143 = 1.027678184 Reorder the terms: -1.142857143 + x3 = 1.027678184 Solving -1.142857143 + x3 = 1.027678184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + x3 = 1.027678184 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x3 = 1.027678184 + 1.142857143 x3 = 1.027678184 + 1.142857143 Combine like terms: 1.027678184 + 1.142857143 = 2.170535327 x3 = 2.170535327 Simplifying x3 = 2.170535327 Reorder the terms: -2.170535327 + x3 = 2.170535327 + -2.170535327 Combine like terms: 2.170535327 + -2.170535327 = 0.000000000 -2.170535327 + x3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x3 + -1.142857143 = -1.027678184 Simplifying x3 + -1.142857143 = -1.027678184 Reorder the terms: -1.142857143 + x3 = -1.027678184 Solving -1.142857143 + x3 = -1.027678184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + x3 = -1.027678184 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x3 = -1.027678184 + 1.142857143 x3 = -1.027678184 + 1.142857143 Combine like terms: -1.027678184 + 1.142857143 = 0.115178959 x3 = 0.115178959 Simplifying x3 = 0.115178959 Reorder the terms: -0.115178959 + x3 = 0.115178959 + -0.115178959 Combine like terms: 0.115178959 + -0.115178959 = 0.000000000 -0.115178959 + x3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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