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Simplifying 6x + 2x2 + -7x + 5 = 12x2 + -30x Reorder the terms: 5 + 6x + -7x + 2x2 = 12x2 + -30x Combine like terms: 6x + -7x = -1x 5 + -1x + 2x2 = 12x2 + -30x Reorder the terms: 5 + -1x + 2x2 = -30x + 12x2 Solving 5 + -1x + 2x2 = -30x + 12x2 Solving for variable 'x'. Reorder the terms: 5 + -1x + 30x + 2x2 + -12x2 = -30x + 12x2 + 30x + -12x2 Combine like terms: -1x + 30x = 29x 5 + 29x + 2x2 + -12x2 = -30x + 12x2 + 30x + -12x2 Combine like terms: 2x2 + -12x2 = -10x2 5 + 29x + -10x2 = -30x + 12x2 + 30x + -12x2 Reorder the terms: 5 + 29x + -10x2 = -30x + 30x + 12x2 + -12x2 Combine like terms: -30x + 30x = 0 5 + 29x + -10x2 = 0 + 12x2 + -12x2 5 + 29x + -10x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 5 + 29x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.5 + -2.9x + x2 = 0.0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -2.9x + 0.5 + x2 = 0.0 + 0.5 Reorder the terms: -0.5 + 0.5 + -2.9x + x2 = 0.0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -2.9x + x2 = 0.0 + 0.5 -2.9x + x2 = 0.0 + 0.5 Combine like terms: 0.0 + 0.5 = 0.5 -2.9x + x2 = 0.5 The x term is -2.9x. Take half its coefficient (-1.45). Square it (2.1025) and add it to both sides. Add '2.1025' to each side of the equation. -2.9x + 2.1025 + x2 = 0.5 + 2.1025 Reorder the terms: 2.1025 + -2.9x + x2 = 0.5 + 2.1025 Combine like terms: 0.5 + 2.1025 = 2.6025 2.1025 + -2.9x + x2 = 2.6025 Factor a perfect square on the left side: (x + -1.45)(x + -1.45) = 2.6025 Calculate the square root of the right side: 1.61322658 Break this problem into two subproblems by setting (x + -1.45) equal to 1.61322658 and -1.61322658.Subproblem 1
x + -1.45 = 1.61322658 Simplifying x + -1.45 = 1.61322658 Reorder the terms: -1.45 + x = 1.61322658 Solving -1.45 + x = 1.61322658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.45' to each side of the equation. -1.45 + 1.45 + x = 1.61322658 + 1.45 Combine like terms: -1.45 + 1.45 = 0.00 0.00 + x = 1.61322658 + 1.45 x = 1.61322658 + 1.45 Combine like terms: 1.61322658 + 1.45 = 3.06322658 x = 3.06322658 Simplifying x = 3.06322658Subproblem 2
x + -1.45 = -1.61322658 Simplifying x + -1.45 = -1.61322658 Reorder the terms: -1.45 + x = -1.61322658 Solving -1.45 + x = -1.61322658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.45' to each side of the equation. -1.45 + 1.45 + x = -1.61322658 + 1.45 Combine like terms: -1.45 + 1.45 = 0.00 0.00 + x = -1.61322658 + 1.45 x = -1.61322658 + 1.45 Combine like terms: -1.61322658 + 1.45 = -0.16322658 x = -0.16322658 Simplifying x = -0.16322658Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.06322658, -0.16322658}
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