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Simplifying 7x2 + 16x = 192 Reorder the terms: 16x + 7x2 = 192 Solving 16x + 7x2 = 192 Solving for variable 'x'. Reorder the terms: -192 + 16x + 7x2 = 192 + -192 Combine like terms: 192 + -192 = 0 -192 + 16x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -27.42857143 + 2.285714286x + x2 = 0 Move the constant term to the right: Add '27.42857143' to each side of the equation. -27.42857143 + 2.285714286x + 27.42857143 + x2 = 0 + 27.42857143 Reorder the terms: -27.42857143 + 27.42857143 + 2.285714286x + x2 = 0 + 27.42857143 Combine like terms: -27.42857143 + 27.42857143 = 0.00000000 0.00000000 + 2.285714286x + x2 = 0 + 27.42857143 2.285714286x + x2 = 0 + 27.42857143 Combine like terms: 0 + 27.42857143 = 27.42857143 2.285714286x + x2 = 27.42857143 The x term is 2.285714286x. 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. 2.285714286x + 1.306122449 + x2 = 27.42857143 + 1.306122449 Reorder the terms: 1.306122449 + 2.285714286x + x2 = 27.42857143 + 1.306122449 Combine like terms: 27.42857143 + 1.306122449 = 28.734693879 1.306122449 + 2.285714286x + x2 = 28.734693879 Factor a perfect square on the left side: (x + 1.142857143)(x + 1.142857143) = 28.734693879 Calculate the square root of the right side: 5.360475154 Break this problem into two subproblems by setting (x + 1.142857143) equal to 5.360475154 and -5.360475154.Subproblem 1
x + 1.142857143 = 5.360475154 Simplifying x + 1.142857143 = 5.360475154 Reorder the terms: 1.142857143 + x = 5.360475154 Solving 1.142857143 + x = 5.360475154 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 + x = 5.360475154 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + x = 5.360475154 + -1.142857143 x = 5.360475154 + -1.142857143 Combine like terms: 5.360475154 + -1.142857143 = 4.217618011 x = 4.217618011 Simplifying x = 4.217618011Subproblem 2
x + 1.142857143 = -5.360475154 Simplifying x + 1.142857143 = -5.360475154 Reorder the terms: 1.142857143 + x = -5.360475154 Solving 1.142857143 + x = -5.360475154 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 + x = -5.360475154 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + x = -5.360475154 + -1.142857143 x = -5.360475154 + -1.142857143 Combine like terms: -5.360475154 + -1.142857143 = -6.503332297 x = -6.503332297 Simplifying x = -6.503332297Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.217618011, -6.503332297}
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