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Simplifying 15x2 + 21x + 7 = 0 Reorder the terms: 7 + 21x + 15x2 = 0 Solving 7 + 21x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.4666666667 + 1.4x + x2 = 0 Move the constant term to the right: Add '-0.4666666667' to each side of the equation. 0.4666666667 + 1.4x + -0.4666666667 + x2 = 0 + -0.4666666667 Reorder the terms: 0.4666666667 + -0.4666666667 + 1.4x + x2 = 0 + -0.4666666667 Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000 0.0000000000 + 1.4x + x2 = 0 + -0.4666666667 1.4x + x2 = 0 + -0.4666666667 Combine like terms: 0 + -0.4666666667 = -0.4666666667 1.4x + x2 = -0.4666666667 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 = -0.4666666667 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = -0.4666666667 + 0.49 Combine like terms: -0.4666666667 + 0.49 = 0.0233333333 0.49 + 1.4x + x2 = 0.0233333333 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 0.0233333333 Calculate the square root of the right side: 0.152752523 Break this problem into two subproblems by setting (x + 0.7) equal to 0.152752523 and -0.152752523.Subproblem 1
x + 0.7 = 0.152752523 Simplifying x + 0.7 = 0.152752523 Reorder the terms: 0.7 + x = 0.152752523 Solving 0.7 + x = 0.152752523 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 = 0.152752523 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 0.152752523 + -0.7 x = 0.152752523 + -0.7 Combine like terms: 0.152752523 + -0.7 = -0.547247477 x = -0.547247477 Simplifying x = -0.547247477Subproblem 2
x + 0.7 = -0.152752523 Simplifying x + 0.7 = -0.152752523 Reorder the terms: 0.7 + x = -0.152752523 Solving 0.7 + x = -0.152752523 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 = -0.152752523 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -0.152752523 + -0.7 x = -0.152752523 + -0.7 Combine like terms: -0.152752523 + -0.7 = -0.852752523 x = -0.852752523 Simplifying x = -0.852752523Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.547247477, -0.852752523}
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