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Simplifying 15x2 + 21x = 5 Reorder the terms: 21x + 15x2 = 5 Solving 21x + 15x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 21x + 15x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 21x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.3333333333 + 1.4x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 1.4x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 1.4x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 1.4x + x2 = 0 + 0.3333333333 1.4x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 1.4x + x2 = 0.3333333333 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = 0.3333333333 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 0.3333333333 + 0.49 Combine like terms: 0.3333333333 + 0.49 = 0.8233333333 0.49 + 1.4x + x2 = 0.8233333333 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 0.8233333333 Calculate the square root of the right side: 0.907377173 Break this problem into two subproblems by setting (x + 0.7) equal to 0.907377173 and -0.907377173.Subproblem 1
x + 0.7 = 0.907377173 Simplifying x + 0.7 = 0.907377173 Reorder the terms: 0.7 + x = 0.907377173 Solving 0.7 + x = 0.907377173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 0.907377173 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 0.907377173 + -0.7 x = 0.907377173 + -0.7 Combine like terms: 0.907377173 + -0.7 = 0.207377173 x = 0.207377173 Simplifying x = 0.207377173Subproblem 2
x + 0.7 = -0.907377173 Simplifying x + 0.7 = -0.907377173 Reorder the terms: 0.7 + x = -0.907377173 Solving 0.7 + x = -0.907377173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -0.907377173 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -0.907377173 + -0.7 x = -0.907377173 + -0.7 Combine like terms: -0.907377173 + -0.7 = -1.607377173 x = -1.607377173 Simplifying x = -1.607377173Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.207377173, -1.607377173}
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