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Simplifying 51 = 14x + 2x2 Solving 51 = 14x + 2x2 Solving for variable 'x'. Reorder the terms: 51 + -14x + -2x2 = 14x + -14x + 2x2 + -2x2 Combine like terms: 14x + -14x = 0 51 + -14x + -2x2 = 0 + 2x2 + -2x2 51 + -14x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 51 + -14x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -25.5 + 7x + x2 = 0 Move the constant term to the right: Add '25.5' to each side of the equation. -25.5 + 7x + 25.5 + x2 = 0 + 25.5 Reorder the terms: -25.5 + 25.5 + 7x + x2 = 0 + 25.5 Combine like terms: -25.5 + 25.5 = 0.0 0.0 + 7x + x2 = 0 + 25.5 7x + x2 = 0 + 25.5 Combine like terms: 0 + 25.5 = 25.5 7x + x2 = 25.5 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 25.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 25.5 + 12.25 Combine like terms: 25.5 + 12.25 = 37.75 12.25 + 7x + x2 = 37.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 37.75 Calculate the square root of the right side: 6.144102864 Break this problem into two subproblems by setting (x + 3.5) equal to 6.144102864 and -6.144102864.Subproblem 1
x + 3.5 = 6.144102864 Simplifying x + 3.5 = 6.144102864 Reorder the terms: 3.5 + x = 6.144102864 Solving 3.5 + x = 6.144102864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 6.144102864 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 6.144102864 + -3.5 x = 6.144102864 + -3.5 Combine like terms: 6.144102864 + -3.5 = 2.644102864 x = 2.644102864 Simplifying x = 2.644102864Subproblem 2
x + 3.5 = -6.144102864 Simplifying x + 3.5 = -6.144102864 Reorder the terms: 3.5 + x = -6.144102864 Solving 3.5 + x = -6.144102864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -6.144102864 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -6.144102864 + -3.5 x = -6.144102864 + -3.5 Combine like terms: -6.144102864 + -3.5 = -9.644102864 x = -9.644102864 Simplifying x = -9.644102864Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.644102864, -9.644102864}
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