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Simplifying 3x2 + -4x + 30 + 7x2 + 6x + -51 = 0 Reorder the terms: 30 + -51 + -4x + 6x + 3x2 + 7x2 = 0 Combine like terms: 30 + -51 = -21 -21 + -4x + 6x + 3x2 + 7x2 = 0 Combine like terms: -4x + 6x = 2x -21 + 2x + 3x2 + 7x2 = 0 Combine like terms: 3x2 + 7x2 = 10x2 -21 + 2x + 10x2 = 0 Solving -21 + 2x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.1 + 0.2x + x2 = 0.0 Move the constant term to the right: Add '2.1' to each side of the equation. -2.1 + 0.2x + 2.1 + x2 = 0.0 + 2.1 Reorder the terms: -2.1 + 2.1 + 0.2x + x2 = 0.0 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + 0.2x + x2 = 0.0 + 2.1 0.2x + x2 = 0.0 + 2.1 Combine like terms: 0.0 + 2.1 = 2.1 0.2x + x2 = 2.1 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 2.1 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 2.1 + 0.01 Combine like terms: 2.1 + 0.01 = 2.11 0.01 + 0.2x + x2 = 2.11 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 2.11 Calculate the square root of the right side: 1.452583905 Break this problem into two subproblems by setting (x + 0.1) equal to 1.452583905 and -1.452583905.Subproblem 1
x + 0.1 = 1.452583905 Simplifying x + 0.1 = 1.452583905 Reorder the terms: 0.1 + x = 1.452583905 Solving 0.1 + x = 1.452583905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 1.452583905 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 1.452583905 + -0.1 x = 1.452583905 + -0.1 Combine like terms: 1.452583905 + -0.1 = 1.352583905 x = 1.352583905 Simplifying x = 1.352583905Subproblem 2
x + 0.1 = -1.452583905 Simplifying x + 0.1 = -1.452583905 Reorder the terms: 0.1 + x = -1.452583905 Solving 0.1 + x = -1.452583905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -1.452583905 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -1.452583905 + -0.1 x = -1.452583905 + -0.1 Combine like terms: -1.452583905 + -0.1 = -1.552583905 x = -1.552583905 Simplifying x = -1.552583905Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.352583905, -1.552583905}
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